•^^^m^mmimmm^m^ 


ARITHMETIC 

WITHOUT  A  PENCIL 
E.M.JOY 


UC-NRLF 


^B    E7fl    2flD 


E>*C-HF2ATH    &    CO.BOSTOr 


^^- 


0 


-f- 


IN  MEMORIAM 
FLORIAN  CAJORl 


Digitized  by  the  Internet  Archive 

in  2Q07  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/arithmeticwithouOOjoyerich 


ARITHMETIC 


WITHOUT    A    PENCIL 


BY 

EDITH   M.    JOY 


And  to  know, 
Rather  consists  in  opening  out  a  way 
Whence  the  imprisoned  splendor  may  escape, 
Than  in  effecting  entry  for  a  light 
Supposed  to  be  without. 

—  BBowNma 


BOSTON,  U.S.A. 

D.    C.    HEATH   &   CO.,   PUBLISHERS 

1904 


Copyright,  1902, 
By  D.  G.  Heath  &  Co. 


FOREWORD 

The  superiority  that  is  claimed  for  this  book  is  based 
upon  its  logical,  easily  progressive,  purposeful  arrangement : 
logical,  because  each  new  principle  or  fact  is  introduced  at 
the  point  at  which  the  need  for  it  appears  ;  easily  progres- 
sive, because  but  one  difficulty  at  a  time  is  presented  and  its 
mastery  leaves  the  student  with  the  power  necessary  to  the 
accomplishment  of  the  next;  purposeful,  because  each  exer- 
cise carries  with  it  a  particular  something  to  be  achieved, 
bearing  directly  upon  the  perfect  whole. 

Teachers  of  Arithmetic  must  bear  in  mind  that  each  new 
phase  of  the  science  should  be  developed  without  the  pencil 
in  the  student's  hand ;  that  Written  Arithmetic  is  logically 
supplementary  to  Mental  Arithmetic;  and  that  all  work 
must  be  systematic,  living,  and  full  of  purpose. 

Let  the  aim  be  clear  reasoning,  accuracy,  and  rapidity ; 
with  steady,  daily  gain  in  each ;  and  let  success  mean,  not  so 
much  the  acquirement  of  knowledge  of  certain  facts  and 
principles,  as  the  development  of  the  power  that  is  within. 

EDITH  M.  JOY. 


iH 


CONTENTS 

PAGE 

Addition 1 

Abstract,  §§  1-37 1 

Complements,  §§  20-25,  29,  30 6,  9 

Counting,  §  37 13 

SUBTKACTION 14 

Abstract,  §§  38-52 14 

Addition  and  Subtraction  —  Concrete,  §§  53-59         ....  20 

Original  Problems,  §  60 27 

Multiplication  and  Division .27 

Abstract  and  Concrete,  §§  61-120 27 

Division  by  Even  Tens,  §§  129-130 65 

To  determine  Number  of  Digits  in  Quotient,  §§  132-134          .        .  67 

Beading  Numbers,  §  128 64 

Fractions 68 

Halves,  §  135 68 

Quarters,  §  136 73 

Eighths,  §  137 75 

Thirds,  §  138 78 

Ninths,  §  139 80 

Sixths  and  Twelfths,  §  140 83 

Fifths  and  Tenths,  §  141 87 

Terms,  Definitions,  and  Explanations,  §  142 88 

Changing  Improper  Fractions  and  Mixed  Numbers,  §  143       .         .  90 

Definitions,  and  Explanations,  leading  to  Factoring,  §§  144-146,  148  92 

Reducing  to  Lowest  Terms,  §  147 97 

Changing  to  Common  Denominator,  §  149 99 

Addition,  Concrete  and  Abstract,  §§  150-159 100 

Multiplication,  Concrete  and  Abstract,  §§  160-169  ....  110 

Division,  Concrete  and  Abstract,  §§  170-173 117 

Relation  of  Numbers  to  Each  Other,  §§  174-178      .        .        .        .122 

iv 


CONTENTS  V 

PAGB 

Decimals 127 

Reading,  §§  179-181 127 

Addition,  Abstract,  §  182 130 

Subtraction,  Abstract,  §  183 131 

Multiplication,  Abstract,  §  184 132 

Division,  Abstract,  §  185 132 

Explanation  of  Rules  for  placing  Point,  §  186          ....  133 

Decimal  System,  §  187 134 

Changing  to  Common  Fractions,  §  188 135 

Changing  from  Common  Fractions,  §§  189,  191        .'      .        .        .  136 

Review,  §  190 137 

Part-taking,  §  191 138 

Relation  of  Numbers  to  Each  Other,  §  192 139 

Application  or  Common  Fractions  and  Decimals,  §§  193-195         .  139 

To  Long  Measure,  §  196 149 

To  Surface  Measure,  §  197 154 

To  Cubic  and  Board  Measures,  §  198 158 

To  Liquid  Measure,  §  199 161 

To  Avoirdupois  and  Troy  Weights,  §  200 162 

Percentage 164 

Relation  between  Part  and  Per  Cent,  §§  201,  203    .        .        .        .164 

What  is  A  %  otB?  §§  202,  206 167 

C  is  what  per  cent  of  B?  §§  204,  207 170 

O  is  ^  %  of  what  ?  §§  205,  208 171 

Miscellaneous,  §§  209-211 173 

Application 177 

To  Profit  and  Loss,  §  212 177 

To  Commission,  §§  213,  214 .179 

To  Duties,  §  215 184 

To  Insurance,  §  216 185 

To  Taxes,  §  217 186 

To  Stocks,  §  218 187 

To  Interest,  §§  219-222 189 

Notes,  §  223 193 

Proportion,  §  224 195 


TO   THE  TEACHER 

An  arithmetical  thought  should  be  developed  bj  means  of 
(1)  concrete  problems  involving  easy  numbers;  after  this 
should  come  (2)  abstract  drill  until  the  pupils  become  so 
skilful  that  in  further  reasoning  they  are  unhampered  by 
the  numbers  ;  following  a  full  comprehension  of  the  thought, 
(3)  problems  should  be  given  whose  solution  requires  use  of 
the  pencil. 

Abridged  illustrations : 

First.  I  spent  10  cents,  which  was  f  of  my  money.  How 
much  money  had  I  ? 

Second.     25  is  |  of  what  number  ? 

Third.  My  father  sold  a  cow  for  |60,  which  was  |^  of  the 
cost.     What  did  he  pay  for  her  ? 

Fourth.  A  store  was  sold  for  1250,200.  This  was  -^  of 
what  was  asked  for  it.     What  was  asked  ? 

Each  new  principle  must  be  dwelt  upon  long  enough  to 
insure  its  becoming  fixed  in  mind.  To  do  this  it  will  be 
necessary  for  pupils  to  solve,  without  pencil,  many  more 
problems  than  are  contained  in  this  book;  These  problems 
he  may  make  for  himself  largely.  Illustrations :  Make  ten 
problems  involving  the  principle  of  No.  20,  Exercise  193, 
and  introducing  as  much  variety  as  possible.  Make  practi- 
cal examples  using  the  numbers  in  No.  16,  Exercise  201. 

The  class  must  be  studied.  Its  needs  will  furnish  the 
inspiration  from  which  will  grow  the  plan  for  the  daily 
lesson.  May  "Arithmetic  without  a  Pencil"  justify  its 
existence  by  proving  to  be  of  assistance  in  the  carrying  out 
of  such  plans.' 

E.  M.  J. 
ii 


ARITHMETIC   WITHOUT   A   PENCIL 


ADDITION 
1 


6 

8 

5 

3 

4 

9 

7 

6 

4 

6 

5 

7 

7 

4 

9 

7 

6 

8 

8 

_3 

7 

6 

6 

7 

8 

2 

7 

8 

7 

5 

4 

4 

9 

6 

7 

4 

5 

9 

_2 

8 

9 

4 

3 

9 

9 

8 

5 

4 

2 

16         18         15         13         14         19         17         16         14 

749768837 


16 

14 

15 

16 

18 

12 

17 

17 

17 

5 

4 

7 

6 

5 

6 

7 

2 

9 

15 

14 

14 

19 

17 

14 

19 

17 

16 

4 

3 

9 

9 

6 

8 

5 

3 

4 

18 

18 

13 

17 

15 

17 

15 

16 

12 

9 

7 

6 

4 

6 

5 

8 

8 

7 

19 

14 

13 

19 

18 

18 

13 

19 

18 

7 

5 

4 

6 

6 

2 

9 

2 

3 

18 

16 

14 

17 

17 

18 

13 

12 

19 

8 

9 

7 

9 

6 

_5 

8 

9 

3 

ARITHMETIC   WITHOUT   A  PENCIL 


9  +  9 

4  +  9 

4  +  3 

3 

5+4 

6+5 

4  +  4 

5  +  7 

6  +  6 

5  +  8 

6  +  2 

7  +  7 

2  +  7 

7  +  9 

4  +  7 

3  +  6 

8  +  7 

9  +  8 

6  +  4 

7  +  3 

9  +  5 

4  +  8 

6  +  7 

3  +  5 

8  +  3 

2  +  9 

5+4 

6  +  3 

4  +  2 

19+  9 

14+  9 

14+  3 

4 

15  +  4 

16  +  5 

14  +  4 

5  +  17 

6  +  16 

5  +  18 

6  +  12 

17  +  7 

12  +  7 

17  +  9 

4  +  17 

3  +  16 

8  +  17 

19+   8 

16  +  4 

17  +  3 

19  +  5 

4  +  18 

6  +  17 

3  +  15 

18+   3 

13  +  3 

12  +  9 

15  +  4 

16+   3 

3       6 

6       3 

2       4 

5 

6 

5       4 

4       4 

8       3 

4       3 

3       8 

3       9 

4 

9       7 

8       7 

2       8 

6       5 

7       2 

6       4 

9 

2       5 

4       2 

1       5 

7 

3 

3 

5 

3 

7 

9 

4 

4 

2 

3 

8 

9 

3 

4 

9 

7 

4 

7 

7 

6 

5 

7 

8 

8 

7 

8 

7 

2 

5 

9 

2 

3 

5 

8 

6 

7 

7 

4 

5 

7 

5 

4 

9 

5 

3 

6 

3 

4 

6 

4 

7 

6 

7 

3 

7 

7 

2 

9 

8 

2 

2 

2 

2 

8 

8 

4 

9 

6 

^ 

7 

3 

7 

6 

6 

5 

5^ 

9 

5 

9 

4 

5 

2 

7 

4 

6 

8 

3 

6 

4 

9 

8 

7 

'  7 

6 

9 

_9 

^ 

4 

7 

7 

6 

7 

3 

6 

5 

2 

7 

2 

5 

4 

4 

9 

6 

8 

6 

5 

8 

6 

7 

7 

4 

3 

9 

9 

4 

7 

2 

3     5 

8 

7 

4 

3 

9 

6 

3 

4 

8     7 

4 

6 

9 

8 

7      9 

3 

8 

9 

9 

9 

6 

5 

4 

5     6 

7 

3 

6 

7 

4      9 

3 

7 

7 

2 

5 

5 

7 

9 

2      3 

4 

5 

ADDITION  8 

6 

3  +  7  +  8   7  +  2  +  5   7  +  3  +  5  6  +  2  +  7  4+4+4 

8+2+7   1+9+6   7+6+4  7+1+4  6+6+6 

6+5+3   3+4+6   8+1+2  4+3+5  9+1+8 

6+4+6   5+2+8   7+2+7  6+1+7  6+8+4 

9+8+2   4+5+3   8+1+9  2+5+6  3+3+7 

4+9+1    6+3+2   5+3+7  3+3+3  4+4+6 

8+6+4   5+3+5   4+4+8  5+5+5  7+7+2 

7 

10          10         10         10         10  10         10  10         20 

687254932 


20 

20 

20 

30 

30 

30 

30 

10 

10 

7 

9 

6 

8 

4 

3 

5 

18 

17 

10 

10 

10 

10 

10 

10 

10 

10 

20 

11 

12 

13 

15 

14 

19 

16 

20 

14 

20 

20 

30 

30 

30 

30 

30 

30 

30 

17 

13 

12 

15 

13 

16 

19 

14 

18 

30 

40 

40 

40 

40 

40 

50 

60 

70 

17 

17 

19 

16 

14 

17 

18 

17 

19 

8 

13   14 

15 

15 

15 

13    13 

14 

11 

15 

12  11   17   11   13   14   15   15   15   18 

13  14   12   11   13   13    14   11    15   11 


14 

15 

14 

11 

11 

13 

12 

12 

17 

11 

14 

12 

12 

12 

16 

11 

12 

16 

13 

17 

13 

13 

13 

13 

18 

14 

15 

19 

15 

16 

15 

16 

14 

19 

12 

18 

16 

11 

17 

11 

4  ARITHMETIC   WITHOUT   A  PENCIL 

9 

20   20    20    20    20    20    80    50   30    30 
10   50    30    60    20    40    20    30    30    40 


50 

60 

40 

40 

50 

60 

70 

90 

95 

75 

30 

30 

40 

50 

50 

40 

30 

10 

5 

25 

75 

50 

25 

85 

70 

30 

20 

40 

85 

85 

15 

25 

25 

15 

30 

50 

80 

50 

5 

15 

10 

26        28        25        23        24        29        27        26        24        26 

7497688  3  75 


24 

25 

26 

28 

22 

27 

27 

27 

24 

24 

4 

7 

6 

5 

6 

7 

2 

9 

3 

9 

29 

25 

27 

28 

23 

27 

29 

29 

28 

27 

9 

8 

8 

5 

8 

6 

5 

7 

8 

7 

11 

17  +  13 

14  +  12 

11  +  11 

13  +  13 

11  +  12 

14  +  13 

11  +  16 

11  +  14 

14  +  14 

16+14 

17  +  12 

15  +  12 

19  +  11 

15  +  14 

12  +  18 

18  +  11 

12  +  13 

15  +  15 

15  +  11 

12  +  12 

13  +  11 

18  +  8 

19  +  7 

18  +  5 

22  +  6 

27  +  9 

26  +  3 

13 

24  +  4 

28+5 

26  +  7 

23  +  7 

24+3 

24  +  7 

25  +  7 

27  +  8 

28  +  4 

27  +  7 

24  +  6 

27+2 

24  +  9 

26  +  5 

26  +  6 

29  +  8 

25  +  9 

29  +  8 

27  +  4 

28  +  7 

29  +  6 

ADDITION 

13 

39 

37 

36 

88 

35   48 

4 

8 

5 

4 

9    5 

5 


42   47   44   47 
9    6    9    4 


55 

56 

54 

58 

58 

61 

68 

68 

65 

69 

7 

8 

5 

9 

8 

8 

8 

9 

6 

9 

14 

71  +  9 

77+8 

75  +  7 

73  +  8 

79  +  5 

76  +  8 

84  +  5 

85  +  6 

81  +  9 

89  +  7 

88  +  5 

86  +  3 

95  +  9 

97+6 

98  +  6 

93  +  8 

96  +  5 

92  +  9 

15 

1234567896397835 
2345678914852  7  86 
3456789122747835 
4567891233235786 


16 

20 

80 

90 

70 

20 

50 

90 

60 

30 

90 

30 

50 

40 

20 

10 

60 

10 

40 

80 

50 

60 

10 

10 

50 

80 

10 

20 

20 

70 

40 

90 

30 

60 

30 

70 

40 

30 

30 

20 

30 

80 

30 

60 

70 

30 

90 

70 

90 

70 

50 

70 

80 

60 

50 

30 

50 

30 

50 

70 

30 

80 

30 

60 

50 

40 

60 

90 

40 

40 

30 

70 

80 

60 

70 

40 
17 

40 

40 

50 

40 

50 

48 

29 

18 

25 

59 

34 

29 

57 

16 

35 

32 

42 

44 

37 

16 

15 

19 

38 

19 

16 

17 

16 

51 

12 

18 

17 

25 

19 

48 

41 

24 

19 

9 

27 

49 

25 

18 

30 

27 

13 

6  ARITHMETIC   WITHOUT  A  PENCIL 

18 

17  19  18   51   18   19  18  13  19  11 

16  11  14   17   17   17  15  15  19  12 
13  15  12   14   18   13  15  15  17  13 

17  18  19   12   19   15  14  17  18  14 
19  11  17   18   16   14  11  12  12  15 

18  13  11   19   19   12  19  18  13  16 
16  17  15   16   15   10  12  11  19  17 


19 

249 

276 

349 

473 

209 

411 

246 

479 

372 

298 

726 

484 

483 

789 

279 

358 

297 

723 

138 

567 

289 

195 

444 

137 

653 

417 

239 

843 

476 

235 

115 

237 

425 

215 

507 

727 

20 

239 

317 

238 

105 

Complements  of  10 

8 

6    1 

7 

4 

9 

5 

2 

3 

7 

5 

2 

4    3 

8 

6 

1 

9 

4 

9 

5 

1 

7 

3    8 

6 

2 

1 

6 

8 

7 

5 

4 

2 

3    9 

5 

8 

9 

2 

1 

6 

3 

7 

4 

6    7 

■  9 

3 

5 

7 

6 

8 

4 

2 

Complements  of  12 

293546871 

11    10     8     2     1    11     9     6     3 

7495    10     218    11 

9764835    10     2 


ADDITION  7 

Complements  of  20 
18         12  5396427 

10         11  7  1  8         13  9         17  5 

13         15  6         14  7         19  3  9  2 

16  9         11  7         13  2         15  4  7 

864         14  6         11389 


— — 

—   — 

— 

21 

Complements  of  25 

20 

10 

15 

24 

12 

18 

11 

7 

•  9 

21  . 

17 

23 

13 

22 

16 

19 

5 

3 

14 

9 

13 

2 

7 

16 

12 

8 

3 

5 

19 

17 

5 

24 

12 

23 

3 

22 

3 

19 

8 

22 

18 

12 

14 

Complements  of  50 

10 

40 

20 

30 

45 

6 

25 

35 

15 

49 

39 

9 

29 

11 

21 

41 

31 

1 

44 

34 

14 

24 

16 

4 

26 

36 

46 

47 

37 

7 

27 

17 

48 

38 

28 

8 

18 

43 

33 

23 

13 

3 

42 

32 

32 

23 

12 

25 

2 

Complements  of  100 

50   75   25 

90    10 

80    20 

40 

60 

30 

70   95   85 

75    6b 

5   15 

25 

35 

45 

ARITHMETIC   WITHOUT   A  PENCIL 


24 

Complements  of  100 

85 

87 

88 

84  •   86 

81 

82 

89 

88 

13 

15 

19 

12 

18   11 

14 

17 

18 

79 

75 

71 

77 

73 

74    76 

72 

78 

25 

27 

29 

21 

24 

26 

23    28 

22 

71 

85 

19 

27 

25 

Complements  of  100 


69    61 

65 

67 

63 

68 

62 

66 

64 

35 

36    34 

31 

39 

38 

32 

33 

37 

55 

b6 

54    53 

57 

58 

52 

51 

59 

41 

49 

48 

42   43 

47 

46 

44 

45 

35 

47 

63 

51 

Add: 

26 

75    50 

95 

15 

76 

99 

96 

71 

18 

83 

25    12 

5 

85 

24 

10 

4 

20 

82 

17 

9    50 

3 

12 

15 

1 

5 

29 

25 

30 

39 

45 

84 

27 

49 

63 

55 

82 

68 

19 

61 

55 

60 

73 

51 

37 

5 

18 

32 

49 

4 

50 

16 

19 

25 

9 

45 

17 

15 

51 

27 


Add: 

19    13 

23 

35 

75 

80 

40 

60 

50 

65        73 

86 

49 

11 

48 

21 

84 

17 

35    27 

14 

51 

81 

52 

79 

16 

83 

35 

95 

29 

45 

31 

28 

49 

88 

29 

52 

66 

9 

29 

45 

31 

28 

49 

88 

29 

18 

34 

91 

71 

55 

69 

72 

51 

12 

71 

48 

ADDITION  » 

28 

Add: 

45        29        56        95        18        24  58        47        27        19 

27        71        44          7        82        25  42        53        73        81 

73        14        13          5        15        75  5          9        25        11 

5          6          9          4          2          5  40        50          5        n 


75 

32 

85 

65 

78 

63 

42 

23 

75 

65 

25 

68 

15 

35 

22 

37 

58 

77 

25 

35 

25 

15 

10 

20 

10 

10 

20 

50 

60 

77 

25 

10 

15 

5 

10 

9 

30 

50 

40 

23 

29 

Complements  of  1000 


500 

900 

100 

200 

800 

700 

300 

400 

600 

750 

250 

350 

650 

750 

450 

150 

850 

950 

50 

990 

10 

20 

980 

970 

30 

40 

960 

920 

930 

960 

940 

910 
30 

80 

60 

70 

970 

Complements 

of  1000 

850 

880 

860 

840 

870 

890 

40 

120 

150 

140 

160 

130 

170 

190 

200 

790 

710 

720 

780 

770 

730 

740 

760 

750 

230 

240 

260 

270 

280 

220 

210 

290 

390 

310 

320 

380 

370 

330 

340 

360 

620 

680 

670 

630 

640 

660 

650 

610 

690 

689 

753 

492 

617 

499 

10  ARITHMETIC   WITHOUT   A  PENCIL 

31 


6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

36 

42 

48 

54 

72 

42 

49 

56 

63 

84 

6 

7 

8 

9 

12 

32 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

48 

56 

64 

,  72 

96 

54 

63 

72 

81 

108 

6 

7 

8 

9 

12 

6 

7 

8 

9 

12 

36  + 

6 

42+  6 

i 

i8  + 

6 

54  + 

6 

60+  6 

42  + 

7 

49+  7 

56  + 

7 

63  + 

7 

70+  7 

48  + 

8 

56+  8 

\ 

64  + 

8 

72  + 

8 

80+  8 

54  + 

9 

63+  9 

72  + 

9 

81  + 

9 

90+  9 

72  +  12 

84  +  12 

< 

96  +  12 

108  +  12 

120  +  12 

ADDITION  11 

33 

60       66       70       80        88       90  99       99       110       121 

6          6          7          8          8          9  9        11          11         11 




— 

— 

— 

— 

~ 

— 

120 

132 

11 

12 

11 

12 

9 

8 

11 

12 

12 

121 

120 

99 
34 

132 

99 

88 

121 

6 

7 

9 

5 

4 

9 

8 

9 

8 

9 

7 

6 

7 

8 

5 

9 

9 

6 

8 

7 

9 

7 

6 

7 

8 

5 

4 

9 

6 

9 

7 

9 

7 

6 

7 

8 

5 

4 

9 

6 

9 

7 

11 

3 

6 

9 

8 

5 

4 

9 

6 

9 

7 

11 

3 

6 

7 

8 

5 

4 

7 

6 

9 

7 

11 

3 

9 

7 

8 

8 

4 

9 

6 

9 

7. 

6859  8                  68956 

6856  85989  57 

6899  12        7789  56 

6896  85988  57 

12        999  12        7789  5        6 

12        9        9         6  12        5        9        8        9  5        7 

~"       "■  9        9  6        6 


1 

8 

9 

6 

8 

7 

9 

5 

8 

9 

6 

6 

9 

8 

9 

6 

8 

6 

9 

7 

3 

9 

7 

8 

9 

6 

9 

8 

6 

8 

8 

6 

6 

6 

9 

8 

9 

7 

7 

9 

7 

6 

5 

7 

7 

8 

9 

6 

9 

8 

7 

6 

8 

4 

6 

6 

9 

8 

9 

7 

8 

8 

6 

5 

8 

8 

7 

8 

9 

6 

6 

7 

7 

8 

8 

9 

7 

12  ARITHMETIC   WITHOUT   A   PENCIL 

35 

7+1+8+9    8+1+6+7  6+2+3+5  9+1+9+7 

6+1+7+8    1+5+6+9  7+7+3+8  7+2+9+6 

8+3+4+7    4+8+7+5  9+3+6+6  6+7+5+8 

9+4+7+6    7+7+6+8  6+8+9+4  9+4+7+7 

7+8+9+6    9+6+7+8  9+7+5+4  3+7+8+3 

4+6+5+5+9+7  6+6+9+3+3+7  7+3+7+8+6+9 
7+8+7+8+6+9  6+8+6+4+6+9  10+4+6+4+5+5 
7+7+7+7+7+3  8+3+7+6+5+9   3+4+7+9+5+2 

2+5+3+4+1+7+9+8  5+3+4+9+1+8+7+2 

2+3+1+9+8+7+4+5  9+4+2+7+6+5+3+8 

2+7+6+5+9+4+8+3  3+8+5+6+4+9+2+7 

9+7+7+6+8+8+5+8  4+8+5+9+7+3+9+8 

36 

Add  horizontally : 

7,  2,  4,  3  4,  9,  6,  2  4,  3,  7,  6,  7,  8,  9 

8,  3,  7,  4  9,  3,  5,  7  5,  7,  2,  8,  3,  6,  4 
5,  7,  9,  3  6,  9,  8,  7  6,  9,  4,  7,  7,  9,  5 
4,  2,  5,  6  3,  7,  9,  8  3,  8,  8,  7,  6,  5,  9 
7,  6,  4,  8  7,  6,  8,  8  9,  7,  1,  3,  2,  5,  8 

17,    9,  11,  15  25,  13,  17,    9  13,  17,    9,    8  15,  25, 15,    9 

12,  13,    7,    6  17,  27,    4,  10  11,  12,  12,  15  75,  50,  45, 12 

4,  19,    2,  15  12,    9,  38,  14  18,    9,  13,  15  37,  20, 17,  ^ 

16,17,11,    8  29,    8,14,42  20,12,15,    7  14,15,16,17 

14,15,    9,12  11,17,18,47  19,19,16,18  9,    7,18,    3 

287,  439  726,  822  473,  728  219,  371  583,  584 

275,  986  496,  117  284,  256  529,  318  728,  472 

335,  481  914,  211  495,  205  417,  482  416,  728 

253,  115  611,  213  129,  482  209,  314  598,  498 


ADDITION  13 

37 

COUNTING 

1.  By  2's  from  50  to  100  and  back. 

2.  By  2's  from  1  to  51  and  back. 

3.  By  2's  from  51  to  99  and  back. 

4.  By  5's  from  0  to  100  and  back. 

5.  By  lO's  from  1  to  121  and  back. 

6.  By  lO's  from  0  to  120  and  back. 

7.  By  lO's  from  2  to  132  and  back. 

8.  By  ll's  from  0  to  132  and  back. 

9.  By  12's  from  0  to  144  and  back. 

10.  By  12's  from  144  to  240  and  back. 

11.  By  3's  from  0  to  52  and  back. 

12.  By  3's  from  1  to  53  and  back. 

13.  By  3's  from  2  to  54  and  back. 

14.  By  4's  from  0  to  100  and  back. 

15.  JBy  4's  from  1  to  101  and  back. 

16.  By  4's  from  2  to  102  and  back. 

17.  By  4's  from  3  to  103  and  back. 

18.  By  6's  from  0  to  102  and  back. 

19.  By  25's  from  0  to  500  and  back. 

20.  By  15's  from  0  to  150  and  back. 

21.  By  7's  from  0  to  91  and  back. 

22.  By  8's  from  0  to  104  and  back. 


14  ARITHMETIC   WITHOUT  A   PENCIL 


SUBTRACTION 

38 

18 

16 

13   17   12   14 

11 

19 

15 

10 

10 

10   10   10   10 

10 

10 

9 

18 

16 

13 

17 

12 

14 

11 

19 

25 

28 

9 

9 

9 

9 

9 

9 

9 

9 

10 

10 

26 

23 

27 

22 

24 

21 

29 

25 

28 

26 

10 

10 

10 

10 

10 

10 

10 

9 

9 

9 

23 

27 

22 

24 

21 

29 

25 

28 

26 

23 

9 

9 

9 

9 

9 

9 

19 

19 

19 

19 

27 

22 

24 

21 

29 

29 

28 

27 

26 

23 

19 

19 

19 

19 

19 

8 

7 

5 

5 

8 

39 

37 

37 

37 

37 

35   35 

35 

35 

48 

48 

10 

9 

19 

29 

10    9 

19 

29 

10 

9 

48 

48 

48 

51 

51 

51 

51 

51 

51 

62 

19 

29 

39 

10 

9 

19 

29 

39 

49 

10 

62 

72 

82 

92 

73 

73 

73 

73 

73 

53 

9 

9 

19 

19 

10 

9 

19 

29 

39 

29 

43 

63 

93 

91 

92 

83 

61 

42 

52 

63 

39 

59 

79 

9 

19 

9 

19 

9 

19 

49 

SUBTRACTION 

16 

40 

11-2   21-2 

31-2 

41-2 

51-2 

61-2   71-2 

81-2   91-2 

101-2 

11-3 

31-3 

51-3   71-3 

81-3   91-3 

21-3 

41-3 

61-3 

101-3   12-3 

22-3   52-3 

62-3 

82-3 
41 

42-3 

72-3   92-3 

21    31    41 

51 

61 

71 

81    91    61 

12    12    12 

12 

22 

22 

22    22    32 

61  61  71  21  31  41  51  61  71 

42  52  32  13  13  13  13  23  33 

61  81  91  91  101  101  22  42  52 

33  33  13  33  63  53  13  13  13 


72    92    102   102   102    82    62    72    53 
13    13    13    23    33    43    33    43    23 


42 

40   40   40   40   40   40   40   40   40   40 
9    1    2    3   13   22   19   11   12   13 


40 

40 

40 

31 

31 

31 

31 

31 

31 

31 

23 

32 

13 

9 

2 

3 

13 

23 

12 

9 

52 

52 

52 

52 

52 

52 

40 

31 

51 

30 

9 

3 

13 

23 

33 

43 

14 

22 

9 

13 

16  ARITHMETIC   WITHOUT   A   PENCIL 


43 

.0 

11 

12 

13 

18   19 

20 

21 

22 

23 

4 

4 

4 

4 

4    4 

4 

4 

4 

4 

28 

29 

20 

21 

22 

23 

28 

29 

40 

51 

4 

4 

14 

14 

14 

14 

14 

14 

24 

24 

72 

63 

97 

98 

27 

31 

52 

66 

86 

36 

24 

34 

54 

84 

14 

14 

24 

34 

44 

14 

44 


10- 

-  5 

80-55 

22- 

-15 

63- 

-35 

84-55 

74-45 

20- 

-  5 

90-45 

32- 

-25 

73- 

-35 

85-55 

72-35 

30- 

-  5 

90-55 

42- 

-15 

73- 

-25 

75-55 

60-15 

40- 

-  5 

11-  5 

52- 

-45 

93- 

-  5 

105-55 

60-35 

50- 

-  5 

21-  5 

62- 

-35 

83- 

-15 

76-15 

49-35 

20- 

-15 

21-15 

72- 

-35 

14- 

-  5 

87-35 

65-35 

30- 

-15 

31-  5 

82- 

-15 

24- 

-15 

48-25 

91-85 

40- 

-15 

31-15 

92- 

-65 

34- 

-  5 

59-15 

47-15 

50- 

-15 

31-25 

13- 

-  5 

44- 

-25 

66-25 

56-25 

50- 

-25 

41-  5 

23- 

-  5 

54- 

-45 

69-55 

81-55 

60- 

-25 

41-15 

52- 

-25 

64- 

-25 

39-25 

72-25 

70- 

-25 

41-25 

53- 

-25 

74- 

-35 

98-35 

63-15 

70- 

-^5 

12-  5 

33- 

-15 

94- 

-15 

91-35 

64-45 

80- 

-45 

22--  5 

63- 

-25 

94- 
45 

-85 

93-35 

51-25 

10 

10 

11 

11 

12 

13 

13 

14 

14   15 

6 

4 

6 

5 

6 

6 

7 

6 

8    6 

15 

25 

35 

45 

25 

35 

45 

24 

34 

44 

9 

6 

16 

16 

16 

16 

16 

6 

6 

6 

SUBTRACTION 

54 

64 

64 

64 

13    23 

23 

6 

16 

26 

36 

6    6 

16 

17 

33        33        43 
16        26        26 


53 

43 

11 

21 

41 

71 

61 

81 

12 

22 

26 

16 

6 

6 

_6 

6 

16 

56 

6 

6 

22 

32 

42 

66 

46 

56 

27 

37 

97 

87 

16 

26 

16 

6 

16 

36 

26 

16 

56 

36 

88 

98 

49 

59 

69 

79 

39 

80 

71 

52 

66 

6 

6 

16 

36 

26 

36 

46 

36 

26 

53 

74 

85 

100 

23 

35 

51 

62 

35 

94 

16 

5Q 

55 

6 

6 

6 

36 

16 

16 

76 

46 

9 

8 

19 

18 

16   15 

14 

13 

12 

11 

7 

7 

7 

7 

7    7 

7 

7 

7 

7 

10 

20 

21 

21 

22 

22 

23 

33 

33 

43 

7 

7 

7 

17 

17 

7 

7 

7 

17 

17 

43 

53 

63 

63 

41 

41 

51 

31 

32 

42 

27 

27 

27 

37 

7 

17 

7 

17 

17 

7 

52 

92 

30 

30 

40 

50 

54 

54 

24 

34 

27 

67 

7 

17 

17 

27 

27 

7 

7 

17 

35 

35 

35 

45 

45 

25 

35 

36 

26 

46 

17 

27 

7 

7 

17 

17 

17 

17 

17 

7 

46 

56 

56 

36 

37 

47 

17 

17 

27 

37 

37 

37 

7 

17 

17 

27 

8 

9 

19 

18 

47 

47 

57 

100 

100 

100 

100 

100 

100 

51 

28 

29 

29 

37 

67 

17 

47 

87 

27 

17 

18  ARITHMETIC   WITHOUT   A  PENCIL 


47 

9 

19 

18 

17 

16    15 

14 

13 

12 

11 

8 

8 

8 

8 

8    8 

8 

8 

8 

8 

11        15        13        20        17        27        27        26        25        21 

375899888  8 

16-8         13-8         14-8         10-8         12-8         15-8 
11  _  8         17-8         15-8         13-8         11-8         12-8 


48 

90        70        60        50        30        80        41        21        91        71 

78        58        48        28        18        38        18        18        68        28 


51 

31 

52 

62 

22 

82 

72 

52 

33 

43 

28 

18 

28 

18 

18 

58 

38 

48 

8 

28 

53 

23 

63 

83 

64 

74 

44 

54 

55 

35 

18 

18 

38 

18 

58 

38 

28 

18 

18 

.  18 

65 

75 

45 

46 

66 

66 

96 

17 

37 

87 

28 

68 

28 

28 

28 

58 

78 

8 

8 

18 

67 

27 

42 

39 

21 

73 

60 

40 

70 

95 

38 

18 

8 

8 

8 

8 

8 

8 

8 

8 

The  number  from  which  another  number  is  taken  is 
called  the  min'-u-end.  The  number  taken  away  is  the 
sub-tra-hend.  The  answer  is  the  re-main-der.  It  is  also 
called  the  dif-fer-ence. 


SUBTKACTION 

ly 

49 

Use  100 

for 

minuend  and 

the 

following  numbers 

for 

subtrahend 

75   86 

74 

73 

77 

78 

72 

71 

79 

45 

36   54 

83 

27 

88 

92 

61 

49 

65 

26 

34   43 

57 

68 

12 

81 

89 

48 

35 

86 

94   23 

37 

48 

32 

41 

19 

55 

16 

24 

63   47 

38 

52 

21 

59 

28 

36 

14 

25 

50 

Find  missing  number  and  tell  whether  it  is  minuend  or 
subtrahend : 
17        16        25        33        39        27        25        42        36        53 

~9~9~8~817~817231519 

21   17   25   33   32   45   100   100   100   100 

12~9        17T8        16"20"85~^~23~45 

100  100   73   49   63   47   69   41   39   75 

16^       ~815        29        17"5l2        2925 

51 

Missing  number  and  give  its  name  : 


? 

17 

18 

15 

19 

17 

16 

25 

25 

50 

25 

9 

8 

12 

9 

18 

24 

50 

100 

25 

17 

? 
17 

16 

29 

16 

49 

72 

63 

20 

40 

85 

18 

29 

17 

15 

49 

18 

64 

71 

60 

15 

20  ARITHMETIC   WITHOUT  A   PENCIL 


52 

49 

62 

25 

38 

82 

45 

27 

17 

57 

28 

75 

19 

38 

Q5 

42 

32 

13 

12 

40 

56 

39 

12 

12 

14 

37 

29 

38 

16 

44 

19 

30 

39 

14 

37 

51 

48 

19 

5Q 

25 

31 

53 

CONCRETE  EXAMPLES.     ADDITION  AND  SUBTRACTION 

1.  How  many  dollars  have  John,  Ray,  and  Field  if  each 
one  has  $7?   18?   |9?   $12? 

2.  How  many  oranges  have  these  boys?  Charlie  has  8, 
James  has  18,  and  Ray  has  10.  ' 

3.  Harry  has  149  and  Herbert  has  $11  more.  How 
much  has  Herbert  ? 

4.  It  is  33  miles  from  Pomona  to  Los  Angeles,  and  18 
miles  farther  to  the  ocean.  How  far  from  Pomona  to  the 
ocean  ? 

5.  Max  rode  15  miles  on  Monday,  12  miles  on  Tuesday, 
and  9  miles  on  Wednesday.  How  far  did  he  ride  during 
the  three  days  ?, 

6.  Julia  paid  8  cents  for  a  copy  book,  5  cents  for  a  note 
book,  and  25  cents  for  a  music  reader.  What  did  she  pay 
for  all  ? 

7.  How  many  eggs  in  one  dozen  and  11  eggs?  In  one 
dozen  and  nine  ? 

8.  There  are  14  pupils  in  the  A  class  and  19  in  the  B 
class.     How  many  in  both  ? 


ADDITION  AND   SUBTRACTION  21 

9.    Walter  put  65  cents  in  the  bank  last  week  and  34  cents 
this  week.     How  much  did  he  deposit  in  both  weeks  ? 

10.  Oscar  weighs  49  pounds  and  Martin  weighs  19  pounds 
heavier.  How  much  does  Martin  weigh?  What  is  the 
weight  of  both  ? 

.    11.    Mary  is  11  years  old.     Her  brother  is  37.     How  much 
older  is  he  ? 

12.  It  is  33  miles  from  Pomona  to  Los  Angeles,  and  18 
miles  from  Los  Angeles  to  Santa  Monica.  How  much  farther 
from  Los  Angeles  to  Pomona  than  to  Santa  Monica  ? 

13.  Laura  is  15  years  old.  Her  mother  is  49.  How  much 
younger  is  Laura  than  her  mother  ?  How  old  was  her  mother 
when  Laura  was  born  ? 

14.  Fannie's  standing  in  spelling  was  89  and  Tom's  98. 
What  was  the  difference  between  them  ? 

15.  How  far  apart  are  two  places  that  are  100  miles  and 
75  miles  re-spec-tive-ly  in  the  same  direction  from  another 
place  ? 

16.  One  boy  has  97  pigeons ;  another  has  59.  How  many 
have  both  ?     How  many  more  has  one  than  the  other  ? 

17.  There  were  75  trees  in  a  certain  grove.  How  many 
were  left  after  19  were  cut  down  ? 

18.  How  much  higher  is  oil  at  90  cents  a  can  than  at 
58  cents  ? 

19.  It  cost  my  father  $  84  to  paint  our  house  this  year. 
Two  years  ago  it  cost  him  $  108.    How  much  more  was  that  ? 

20.  It  is  95  rods  around  a  certain  field  and  47  rods  around 
another.  How  much  farther  around  the  first  than  around  the 
second  ? 


22  ARITHMETIC   WITHOUT   A  PENCIL 

21.  If  Thomas  earns  10  cents  on  Monday,  15  cents  on 
Tuesday,  and  20  cents  on  Friday,  how  many  cents  does  he 
earn  in  the  three  days  ? 

22.  If  Carrie  gathers  7  eggs  on  Wednesday,  8  on  Thursday, 
and  12  on  Friday,  how  many  does  she  gather  in  the  three 
days? 

23.  A  man  travelled  12  miles  on  one  day,  15  miles  on  the 
next  day,  and  9  miles  on  the  next  day.  How  far  did  he 
travel  in  the  three  days  ? 

24r.  Robert  gives  25  minutes  to  arithmetic,  20  minutes  to 
spelling,  and  30  minutes  to  reading.  How  many  minutes 
does  he  give  the  three  lessons  ? 

25.  A  farmer  has  15  orange  trees,  12  lemon  trees,  9  peach 
trees,  and  11  pear  trees.     How  many  trees  in  all  ? 

54 

^ h i ^ 

1.  From  A  to  C  is  12  miles.     From  A  to  B  is  50  miles. 
How  far  from  C  to  B  ? 

2.  From  A  to  B  is  51  miles.     From  A  to  D  is  39  miles. 
How  far  from  D  to  B  ? 

3.  From  A  to  C  is  25  miles;   to  D  is  12  miles  farther. 
It  is  100  miles  from  A  to  B.     How  far  from  D  to  B? 

4.  From  C  to  D  is  15  miles;  from  D  to  A  is  38  miles. 
What  is  the  distance  from  A  to  C  ? 

5.  A  and  B  are  75  miles  apart;    A  and  C  18;    and  C 
and.  D  27.     How  far  apart  are  D  and  B  ? 


ADDITION  AND   SUBTRACTION  23 

55 


^  I         a 

B         X  •  z       y 


B  to  A  is  20  feet.     ^  to  (7  is  30  feet. 

1.  Az  \^  ^  feet.     How  long  is  Bz  ?     CL  ? 

2.  ^a;  is  9  feet.     How  long  is  xz  ?     Bx  ?     Ob  ? 

3.  Ay  is  7  feet.     How  long  is  zy  ?     a;^  ?     ^?/  ?     (7y  ? 

4.  Which  is  longer,  a;^  or  Ay  ?     Cx  or  By  ? 

56 

1.  How  far  apart  are  two  boys  who  have  ridden  26  miles 
and  34  miles  in  opposite  directions  from  the  same  place  ? 

2.  Two  towns  are  63  miles  and  48  miles  respectively 
north  of  San  Francisco.     How  far  apart  are  they  ? 

3.  Ned  lives  17  blocks  east  of  the  schoolhouse  and  George 
18  blocks  west.     How  far  from  Ned's  home  to  George's  ? 

4.  One  ship  has  sailed  100  miles  and  another  83  miles  in 
the  same  direction.     How  far  apart  are  they? 

5.  The  depot  is  48  blocks  from  our  house.  The  post- 
office  is  29  blocks  from  our  house  in  the  same  direction. 
How  far  apart  are  the  depot  and  the  post-office  ? 

57 

Find  how  far  around: 


1.  Room  10  feet  wide  and  15  feet  long. 

2.  Lot  50  feet  in  width,  112  feet  in  depth. 

3.  Field  70  rods  wide  and  95  rods  long. 

4.  Farm  140  rods  wide,  300  rods  long. 

5.  How  far  around  a  room  15  ft.  wide  and  18  ft.  long  ? 

6.  How  far  around  a  room  17^  ft.  wide  and  20  ft.  long  ? 


24  ARITHMETIC   WITHOUT   A   PENCIL 

58 

1.  May  had  $1  in  the  bank.  She  drew  out  45  cents. 
How  much  had  she  still  in  bank  ? 

2.  Monroe  has  15  cents  and  he  is  going  to  earn  enough  to 
make  $  1.     How  much  must  he  earn  ? 

3.  I  bought  goods  to  the  amount  of  69  cents.  I  gave  a 
half  and  a  quarter  of  a  dollar  in  payment.  What  change 
should  I  receive  ? 

4.  The  Chronicle  costs  Q5  cents  a  month.  If  I  give  the 
collector  $  1,  what  change  should  he  give  me  ? 

5.  My  dinner  at  the  restaurant  cost  35  cents.  What 
change  should  be  given  me  if  I  give  a  dollar  in  payment? 

6.  A  boy  had  35  rabbits  and  sold  15.  How  many  had 
he  left  ? 

7.  Charles  had  120  feet  of  twine  for  his  kite  and  lost 
19  feet.     How  much  had  he  left  ? 

8.  A  farmer  had  30  acres  of  meadow  land  and  sold  15 
acres.     How  many  acres  had  he  left  ? 

9.  May  is  reading  a  book  containing  48  pages.  She  has 
read  20  pages.     How  many  remain  to  be  read  ? 

10.  There  are  30  days  in  June.     How  many  days  are  left 
after  the  11th? 

11.  There  are   31  days  in  December.     How  many  days 
after  Christmas? 

12.  Max  had  5  dozen  eggs.     He  sold  26.     How  many  had 
he  left  ? 

13.  Raymond  had  1 50  in  the  bank.     He  drew  out  $19. 
How  much  had  he  left  ? 

14.  If  I  sleep  9  hours  out  of  the  —  hours  in  a  day,  how 
many  hours  are  left  for  work  and  play  ? 


ADDITION  AND   SUBTRACTION  25 

15.  A  girl  missed  7  words  out  of  60.  How  many  did  she 
spell  correctly  ? 

16.  How  many  years  before  an  eight-year-old  boy  will 
be  21? 

17.  Carrol  put  f  17  in  the  bank  last  month  and  before  he 
did  so  he  had  $  25  there.  How  much  has  he  there  now  if  he 
has  not  drawn  any  out  ? 

18.  August  has  $37  in  the  bank  and  Conrad  has  $50. 
How  much  more  has  Conrad  than  August  ? 

19.  James  spent  20  cents  for  stamps,  15  cents  for  pens,  and 
25  cents  for  paper.     How  much  did  he  spend  in  all  ? 

20.  Fred  had  one  dollar.  He  spent  87  cents.  How  much 
had  he  left  ? 

59 

1.  Frank  and  Arthur  own  25  acres  of  land  each.  How 
much  less  than  100  acres  does  each  own  ?     Do  both  ? 

2.  100  -  (25  +  25)  =  ?      100  -  25  -  25  =  ? 

3.  From  a  kite  string  48  yards  long,  15  yards  were  lost 
at  one  time  and  13  yards  at  another  time.  How  many  yards 
remained  ? 

4.  48  _  15  -  13  =  ?      48  -  (15  -f  13)  =  ? 

5.  Roy  had  $  100  in  the  bank.  He  drew  out  at  different 
times,  ilO,  $15,  and  $9.     How  much  was  left? 

6.  100  -  (10  -f  15  4-  9)  =  ?       100  -  10  -  15  -  9  =  ? 

7.  A  man  had  75  tons  of  hay.  He  sold  45  tons  and  then 
bought  17  tons  more.      How  many  tons  had  he  then  ? 

8.  75-45  +  17=?       (75  -  45) -f  17  =  ? 

9.  Mr.  Day  had  19  horses  and  bought  57  more.  He  then 
sold  45  of  them.     How  many  had  he  left  ? 


26  ARITHMETIC    WITHOUT   A   PENCIL 

10.  100  -  (25  +  35)  =  ?  100  -  25  -  35  =  ?  [Notice  care- 
fully use  of  parenthesis  marks.] 

11.  In  a  certain  farm  of  100  acres,  17  acres  were  orchard, 
18  acres  were  grain  field,  and  the  remainder  was  pasture. 
How  many  acres  of  pasture  were  there  ? 

12.  It  took  30  yards  to  carpet  one  room,  25  yards  to  car- 
pet another,  and  47  yards  for  a  third  room.  How  much 
more  than  100  yards  did  the  three  rooms  require  ? 

13.  After  cutting  a  certain  number  of  yards  from  a  bolt  of 
ribbon  containing  20  yards,  9  yards  were  left.  How  many 
yards  were  cut  ? 

14.  Conrad  earned  at  different  times,  1 17  and  $25  and 
i30.  He  received  1 18  as  a  present.  How  much  more  did 
he  earn  than  was  given  to  him  ? 

15.  There  are  30  days  in  June  and  31  days  in  July.  If 
I  spend  19  days  out  of  these  two  months  at  the  beach,  and 
12  days  in  the  mountains,  and  the  remainder  of  the  time 
at  home,  how  many  days  do  I  spend  at  home  ? 

16.  Arnold  has  in  his  library  14  books  on  history,  17  story 
books,  12  on  sci^-ence,  9  on  the  lives  of  great  men,  and  5 
picture  books.  How  many  more  should  he  have  to  make  75 
books  ? 

17.  There  are  320  rods  m  a  mile.  From  my  house  to 
Mary's  is  60  rods,  from  her  house  to  Julia's  is  90  rods.  If 
we  walk  from  my  house  to  Julia's,  how  much  farther  must 
we  walk  to  walk  a  mile  from  my  house  ? 

18.  There  are  160  square  rods  in  an  acre.  A  certain 
garden  contains  an  acre ;  70  square  rods  are  planted  in  vege- 
tables and  the  remainder  except  25  square  rods  in  flower 
beds.     How  many  square  rods  in  flower  beds  ? 


MULTIPLICATION   AND  DIVISION  27 

19.  The  minuend  in  a  certain  example  is  1000  ;  the  dif- 
ference is  780.     What  is  the  subtrahend  ? 

20.  (15 +  16 +  14)- (32 +  9)=?     19  +  17-8-17  +  36=? 

60 

Make  examples  in  which  you  use  the  following : 


1. 

75  _  39 +  18  =  ? 

2. 

15  +  8  + 12  +  ?  =  100 

3. 

18  +  7  +  13  =  ? 

4. 

9  +  3  +  7  +  8  =  25 

5. 

45_(20  +  5)=? 

6. 

45  _  20  -  5  =  ? 

7. 

12  +  13  -  15  +  8  =  ? 

8. 

84  -  ?  =  50  +  8 

9. 

19  +  3  =  100  -  ? 

10. 

(7  +  8)-(4  +  9)=? 

Ll. 

(100 -25) +  (75 -3)=? 

12. 

(100  -  49)  +  13  =  ? 

MULTIPLICATION  AND  DIVISION 

61 

Multiply : 

432642  11         7         12         6 

4*593510^         3         _24 

89578792  10  7 

33522222  84 


3x3        3x   5        4x3        4x4        5x   5        3x6  5x4 

9x2        2x12         6x4        3x7        8x    3        8+2  7x2 

7x4        2x11        3x9        2x2        2x10        9x2  5x5 

63 

2)24       3)24     4)24     6)24       8)24     12)24     2)20  4)20 

5)20     10)20     3)21     7)21       2)22     11)22     5)25  2^6 


28 


ARITHMETIC   WITHOUT   A  PENCIL 


64 

18^2  =  ? 

15-h3  =  ?        14 

■^2  =  ? 

28^7  = 

=  ?       18-^3  =  ? 

16h-2  =  ? 

27-^3  =  ?        28 

^2=? 

18^6  = 

=  ?        16-^2  =  ? 

27-^9  =  ? 

26-^2  =  ?        18 

^9  =  ? 
65 

16^8  = 

=  ?       21-7  =  ? 

12=?x? 

12=         14  = 

15  = 

16  = 

16=        18  = 

18  =  ?x? 

20=         20  = 

21  = 

22  = 

24=        24  = 

24  =  ?x? 

25=         26  = 

27  = 
66 

28  = 

18=        30  = 

4x7+1=? 

7x    3+2=? 

5x 

5  +  4  =  ? 

9x    3+1=? 

4x6+2=? 

4x    7+3=? 

3x 

8  +  1  =  ? 

2x12  +  1  =  ? 

5x4+2=? 

5x   5+1=? 

3x 

9  +  2  =  ? 

3x   8+2=? 

2x8+1=? 

2x10  +  3=? 

3x 

4  +  3  =  ? 

4x    7+3=? 

67 


7)24      4)26      7)31      5)29      8)25      2)25     4)30      6)29 
3)26      4)25      7)29      4)17      8)17      8)29      5)31      7)30 


68 

2x10 

3x10 

4x10 

5x 

10 

6x10 

7x10 

8x10 

9x10 

10x10 

2x 

11 

3x11 

4x11 

5x11 

6x11 

7x11 

8x 
69 

11 

9x11 

10x11 

50  =  ?x? 

30  = 

70  = 

90  = 

22  = 

44  = 

88= 

77  =  ?x? 

40  = 

80  = 

100  = 

60  = 

66  = 

55  = 

33  =  ?x? 

99= 

20  = 

80  = 

100  = 

:           110  = 

MULTIPLICATION   AND   DIVISION  29 


70 

51-10 

32-10 

73-10       24-11 

34^11 

56-4-11 

43^10 

89^10 

95^10       45-r-ll 

68-5-11 

100 -4-11 

71 

2)21       3)35       4)45      4)41       5)52  5)58  6)61  6)63 

6)68       7)71       7)78       7)80       8)83  8)89  8)90  9)100 

9)95       9)27       7)28       7)29       9)29  3)22  7)23  8)25 


72 

2x5  =  ? 

4x   5  =  ? 

5x5  =  ? 

25=?x? 

10  =  ?x? 

25  +  5  =  ? 

5x   6  =  ? 

6x5  =  ? 

35  =  ?  X? 

20  =  ?x? 

30  +  5  =  ? 

5x   7  =  ? 

7x5=? 

45  =  ?x? 

30  =  ?x? 

35  +  5  =  ? 

5x   8=? 

8x5  =  ? 

55=^?  X? 

40  =  ?x? 

40  +  5  =  ? 

5x    9  =  ? 

9x5  =  ? 

15=?x? 

50  =  ?x? 

45  +  5  =  ? 

5x10  =  ? 

10x5  =  ? 

5=?x? 

60=?x? 

50  +  5  =  ? 

5x11  =  ? 

11x5  =  ? 

55+5  =  ? 

5x12  =  ? 

12x5  =  ? 

73 

Count  by  5's  from  0  to  60  and  back. 
Count  by  lO's  from  0  to  100  and  back. 
Count  by  ll's  from  0  to  99  and  back. 
Count  by  2's  from  0  to  50  and  back. 

74 
5)31      5)36      5)42      5)46      5)63      5)58      5)37      5)44 

5)48      5)49      5)26      5)29       8)25       8)41       7)29       7)36 


30  ARITHMETIC   WITHOUT   A   PENCIL 

75 

Count  by  2's  from  50  to  100.  Count  by  5's  from  60  to  100. 
Count  the  same  backwards.         Count  the  same  backwards. 

76 

1.  If  3  pounds  of  candy  cost  21  cents,  what  does  one 
pound  cost? 

2.  If  5  pounds  of  peaches  cost  25  cents,  what  does  one 
pound  cost  ? 

3.  If  4  yards  of  ribbon  cost  32  cents,  what  does  one  yard 
cost  ? 

4.  If  7  pounds  of  figs  cost  35  cents,  what  does  one  pound 
cost  ? 

5.  If  8  quarts  of  milk  cost  40  cents,  what  does  1  quart 
cost? 

6.  If  one  box  of  oranges  costs  12,  what  will  3  boxes  cost  ? 

7.  If  one  yard  of  ribbon  costs  10  cents,  what  will  5  yards 
cost? 

8.  If  one  pound  of  grapes  costs  2  cents,  what  will  7  pounds 
cost? 

9.  If  one  pound  of  candy  costs   20   cents,  what  will  2 
pounds  cost  ? 

10.   If  one  yard  of  lace  costs  7  cents,  what  will  5  yards 
cost  ? 

77 

5)65  5)70  5)75  5)80  5)85  5)90  5)95  5)10 
2>20  2)30  2)40  2)50  2)60  2)70  2)80  2)90 
2)22       2)32       2)42       2)52       2)62      2)72       2)82      2)92 


MULTIPLICATION   AND   DIVISION 


31 


24-f-2 
94-2 
86-^2 

78-^-2 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 
cents. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
dimes. 
17. 
18. 
for  — 


34-i-2 

26-T-2 
96^2 
88-V-2 


44-V-2 
36-^2 

28-^2 
98^2 


78 

54-2 
46-^2 

38-2 
36^2 

79 


64-2 
56-2 

48-V-2 
94-2 


74^2 

66^2 

58^2 
96^2 


84-2 
76^2 
68-^2 
88-^2 


10  cents  will  pay  for 
20  cents  will  pay  for 
Twenty  cents  are  — 
30  cents  are dimes,  or 


—  car  rides  at  5  cents. 

—  car  rides  at  5  cents, 
dimes,  or nickels. 


nickels. 


Thirty  cents  are nickels  more  than  a  dime. 

Mary  has  2  dimes  and  a  nickel.     She  has cents. 

She  can  take car  rides  for  her  money. 

Ray  has  4  equal  pieces  of  money,  amounting  to  forty 

They  are . 

5  dimes  are  equal  to nickels. 

Half  a  dollar  is cents. 

It  will  pay car  fares  at  5  cents. 

are  a  quarter  of  a  dollar. 

50  cents  are  equal  to quarters. 

4  dimes  and  a  nickel  are cents. 

Thirty-five  cents  equal dimes  and nickel. 

At  a  nickel  apiece  James  can  get papers  for 


nickels  are 


At  5  cents  a  quart, 
—  cents. 


cents. 

—  quarts  of  milk  can  be  bought 


32  ARITHMETIC   WITHOUT   A  PENCIL 

19.  If  1  box  of  berries  costs  10  cents, boxes  cost 

cents. 

20.  At  15  cents  a  box,  3  boxes  of  berries  will  cost 

cents. 

21.  Ray  has  in  his  bank  2  dimes,  3  nickels,  and  7  pennies. 
He  has cents. 

22.  Fanny  bought  7  yards  of  ribbon  at  a  half-dime  a  yard. 
The  ribbon  cost cents. 

23.  She  gave  50  cents  to  pay  the  bill,  so  she  received 

cents  in  change. 

24.  If  it  costs  25  cents  to  go  to  Pasadena  and  return,  how 
many  trips  can  I  make  for  one  dollar  ? 

25.  What  will  5  trips  cost  ? 

26.  At  10  cents  a  basket,  how  many  baskets  of  oranges 
will  one  dollar  buy  ? 

27.  The  News  is  2  cents.  How  many  papers  can  I  buy 
for  40  cents  ? 

28.  When  ribbon  is  11  cents  a  yard,  what  will  9  yards 
cost  ? 

29.  To  how  many  children  can  I  give  10  pieces  of  candy 
each  if  I  have  73  pieces  ?     How  many  pieces  will  be  left  ? 

30.  79  cents  are  equal  to  how  many  nickels  and  pennies  ? 

31.  There  are  11  girls  in  my  class.  I  bought  70  cherries 
for  them.  How  many  can  I  give  each  ?  How  many  shall  I 
have  left  ? 

32.  How  much  money  are  5  dimes  and  5  half -dimes  ? 

33.  Carrie  had  60  cents.  She  bought  11  yards  of  ribbon 
at  4  cents  a  yard  and  paid  two  car  fares  at  5  cents  each. 
How  much  had  she  left  ? 


MULTIPLICATION   AND  DIVISION  33 

34.  5  pounds  of  candy  at  15  cents  a  pound  will  cost  how- 
much  ? 

35.  Two  dozen  pennies,  two  dimes,  and  two  nickels  are 
how  much  money  ? 

36.  There  are pints  in  1  quart.     There  are pints 

in  2  quarts.     There  are pints  in  5  quarts.     There  are 

pints  in  10  quarts.     There  are pints  in  12  quarts. 

There  are  pints  in  ^  quart.      There  are pints  in 

1|-  quarts.     There  are  pints  in  9  quarts.     There  are 

pints  in  11  quarts. 

37.  There  are  14  pints  in quarts.     There  are  18  pints 

in quarts.     There  are  24  pints  in quarts.     There 

are  40  pints  in  quarts.     There  are  28  pints  in  

quarts.     There  are  64  pints  in quarts.     There  are  100 

pints  in quarts. 

80 

2  pt.)12  pt.  2  pt.)50  pt.  2  pt.)44  pt. 

6,  or  6  qt.  ?,  or  ?  qt.  ?,  or  ?  qt. 

2  pt.)48  pt.  2  pt.)34  pt.  2  pt.)36  pt. 

?,  or  ?  qt.  ?,  or  ?  qt.  ?,  or  ?  qt. 

2  pt.)38  pt.  2  pt.)60  pt. 

?,  or  ?  qt.  ?,  or  ?  qt. 

81 

7  qt.  = pt.  9  qt.  = pt.  8  qt.  = pt. 

qt.  =  24  pt.         qt.  =  42  pt.  qt.  =  84  pt. 

i  qt.  = pt.  IJ  qt.  = pt.  21  qt.  = pt 

5J  qt.  = pt.         qt.  =  25  pt.  qt.  =  21  pt. 


34  ARITHMETIC    WITHOUT   A  PENCIL 

82 

1.  At  5  cents  a  pint,  what  will  3  quarts  of  berries  cost  ? 

2.  At  10  cents  a  quart,  what  will  6  pints  of  %dnegar  cost  ? 

3.  At  10  cents  a  quart,  what  will  3  pints  of  vinegar  cost  ? 

4.  At  10  cents  a  pint,  what  will  10  quarts  of  syrup  cost  ? 

5.  Monroe  picked  berries  at  2  cent  a  pint,  earning  one 
dollar.     How  many  quarts  did  he  pick  ? 

6.  If  these  berries  were  sold  at  10  cents  a  pint,  what  did 
they  bring  ? 

83 

1.  In  1  gallon  there  are  4  quarts.     In  2  gallons  there  are 
quarts. 

2.  In  3   gallons  there  are  quarts.     In  12  gallons 

there  are  quarts. 

3.  In   7   gallons  there  are  quarts.      In  20  gallons 

there  are quarts. 

4.  In  11  gallons  there  are quarts. 

84 

1.  5  gallons  are  equal  to  20  quarts.      gallons  are 

equal  to  28  quarts. 

2.   gallons  are  equal  to  40  quarts.     gallons  are 

equal  to  44  quarts. 

3.   gallons  are  equal  to  24  quarts.     60  quarts  are 

equal  to gallons. 

4.  100  quarts  are  equal  to gallons.     80  quarts  are 

equal  to gallons. 


MULTIPLICATION   AND   DIVISION  36 

85 

1.  Two  pints  of  olives  were  sold  from  a  gallon.     How 
many  quarts  remained  ? 

2.  How  many  quarts  of  oil  in  a  5-gallon  can?     How 
many  pints  ? 

3.  If  one  can  costs  80  cents,  how  much  per  pint  was  it  ? 

4.  When  milk  is  8  cents  a  quart,  and  I  drink  a  pint  each 
day,  in  how  many  days  will  I  drink  a  dollar's  worth  of  milk  ? 

5.  41  quarts  are gal.  and qt.  over. 

6.  29  qt.  are gal.  and qt.  over. 

7.  80  qt.  are gal.  and qt.  over. 

8.  What  will  2  gallons  2  quarts  of  oil  cost  at  2  cents  a 
pint? 

9.  My  lamp  holds  a  quart.     How  many  times  can  I  fill  it 
from  15  gallons  ? 

10.  28  qt.  -T-  4  qt.  =  T,  or  7  gallons. 

11.  44  qt.  -r-  4  qt.  = ,  or gallons. 

12.  20  qt.  -?-  4  qt.  = ,  or gallons. 

13.  80  qt.  -!-  4  qt.  = ,  or gallons. 

14.  88  qt.  -5-  4  qt.  =  ,  or gallons. 

15.  96  qt.  -=-  4  qt.  = ,  or gallons. 

16.  4qt.)100  qt.  17.   4  qt.)200qt. 

?  =  ?  gallons.  ?  =  ?  gallons. 

18.   4  qt.  )240  qt.  19.   4  qt.  )160  qt. 

?  =  ?  gallons.  ?  =  ?  gallonSo 

20.    How  many  gallons  in  200  quarts  ? 


36  ARITHMETIC   WITHOUT   A   PENCIL 

86 

1.  Since  1  yard  equals  3  feet,  2  yards  equal feet. 

2.  Since  1  yard  equals  3  feet,  10  yards  equal feet. 

3.  Since  1  yard  equals feet,  9  yards  equal feet. 

4.  Since  1  yard  equals feet,  8  yards  equal feet. 

5.  Since  there  are  3  ft.  in  1  yd.,  in  30  ft.  there  are yd. 

6.  Since  there  are ft.  in  1  yd.,  in  33  ft.  there  are 

yd. 

7.  Since  there  are ft.  in  1  yd.,  in  21  ft.  there  are 

yd. 

8.  3  ft.)27  ft.       9.  3  ft.)21  ft. 

?  =  ?  yd.  ?  =  ?  yd. 

10.  ft.  yd. 

3  =  11.  3  ft.  13.  21  (yd.) 

9  =  7  (yd.)  J  ft. 

=  3  ft.  ft. 

=  9 

=  10         12.  12  (yd.)       14.  17  (yd.) 
45=  _3ft.       '      S_it. 

27=    '  ft.  ft. 

12  = 
=  7 

87 

1.  At  10  cents  a  foot,  what  does  1  yd.  of  braid  cost  ? 

1  yd.  =  3  ft.  If  1  ft.  =  10  cents,  3  ft.  =  3  x  10  cents,  or 
30  cents.  Therefore,  at  10  cents  a  foot,  1  yd.  of  braid  costs 
30  cents. 

2.  At  5  cents  a  foot,  what  do  2  yards  of  braid  cost  ? 

3.  At  9  cents  a  foot,  what  does  1  yard  of  rope  cost  ? 

4.  At  a  dime  a  foot,  what  do  3  yards  of  wire  cost  ? 


MULTIPLICATION   AND   DIVISION  87 


88 

12  +  2  = 

2)12 

J  of  12  = 

20  +  2  = 

2)20 

Jof  20  = 

14  +  2  = 

2)14 

lof  14  = 

12  +  3  = 

3)12 

iofl2  = 

15  +  3  = 

3)15 

lof  15  = 

1.  I    divided    12  oranges  equally  between   two   sisters. 
How  many  did  I  give  each  ? 

2.  Vern  had  12  apples  and  he  gave  away  ^  of  them.    How 
many  did  he  give  away  ? 

3.  I  picked  J  of  20  boxes  Df  oranges.     How  many  boxes 
did  I  pick  ? 

4.  If  3  pencils  cost  15  cents,  what  does  1  cost  ?     Since  3 
pencils  cost  15  cents,  one  costs  ^  of  15  cents,  or cents. 

5.  If  3  pencils  cost  12  cents,  what  does  1  cost  ? 

6.  J^ofeO?    70?    100?    40?    80? 

7.  ^%of60?    70?    100?    40?    80? 

8.  ^Q  of  20  ?    30  ?    100  ?    10  ? 

9.  i-ofl5?    25?    35?    45?    55? 
10.   f  ofl5?    25?    35?    45?    35? 

11.  How  many  cents  in  |^  of  a  dollar  ? 

12.  In  I?    f?     *?    f? 

13.  How  many  cents  in  -^  of  one  dollar? 

14.  In^?    ^?    ^?    fs? 


38  ARITHMETIC   WITHOUT  A  PENCIL 

15.  If  4  whistles  cost  16  cents,  what  does  1  cost  ? 

16.  1  of  12  =  ?      iofl2  =  ?     I  of  12=?     I  of  12  =  ? 
f  of  12  =  ?  , 

17.  lofl2  =  ?     f  ofl2=?     fofl2  =  ? 


90 

12 

Add: 

12 

2x12 

12  X  2            30 

5x5 

Qx5 

12 

3  xl2 

6 

5x6 

6xQ 

Add: 

Multiply : 

27 

3x9 

9x3                    12 

6           9 

4 

9 

4x9 

r    3x 
4  X 

9x4                     3 

6           4 

9 

36  = 

6  X 

9  X 

12  X 

3)36         4)36         6)36 

9)36 

12^6 

3)36 

3)37 

3)38      4)36      4)37       4>38       4)39 

6)36 

6)37 

6)38 

6)39      9)36      9)39     12)36     12)39 

12}40 

91 

1.  How  many  are  3  dozen  oranges  ? 

2.  There  aye  12  inches  in  1  foot.     How  many  inches  in 
3  feet  ? 

3.  How  many  quarts  are  there  in  9  gallons  ? 

4.  At  6  cents  a  dozen,  what  will  8  dozen  lemons  cost  ? 

5.  Five  lO's  are  how  many  more  than  4  dozen  ? 

6.  At  12  cents  a  foot,  what  does  1  yard  of  wire  cost  ? 

7.  At  4  cents  apiece,  how  many  tops  will  cost  36  cents  ? 


MULTIPLICATION   AND   DIVISION  39 

8.  J  of  36  =  ?        J  of  36  =  ?        iof36  =  ?        ^of36  =  ? 
^V  of  36  =  ? 

9.  I  of  36  =  ?      I  of  36=?      ^of36=?      -/2of36  =  ? 

10.  If  3  babies  of  equal  weight  weigh   36  pounds,  what 
does  one  weigh? 

11.  Earl  earned  ^  of  i  36.     How  much  was  that  ? 

12.  How  many  inches  in  J  of  a  yard  ? 

92 

1.  3x8  =  ?      24  +  8=?      4x8=?      4x7  =  ?      28  +  4=? 
8x4  =  ? 

2.  Eight  4's  are  how  many  ?     6.  Four  8's  are  how  many? 

3.  ^  of  32  are  how  many  ?         7.  What    is    one-fourth   of 

4.  How  many  8's  in  32  ?  thirty -two  ? 

5.  How  many  2's  in  32  ?  8.  How  many  4's  in  32  ? 

*9.  5x7=?      35  +  7=?      6x7=?      6x6=?      36  +  6  =  ? 
7x6=? 

10.  i  of  42  =  ?       {  of  42  =  ?       f  of  42  =  ?       |  of  42=  ? 

11.  What  is  five-sixths  of  42  ? 

12.  What  is  five-sevenths  of  42  ? 


1.  If  seven  copy-books  cost  42  cents,  what  does  one  cost  ? 

2.  At  7  cents  a  piece,  how  many  note-books  will  cost  42 
cents  ? 

3.  How  many  quarts  in  8  gallons  ? 

4.  How  many  days  in  six  weeks  ? 


40 


ARITHMETIC   WITHOUT   A   PENCIL 


11x4=?    44  +  4=? 


94 

1.  3x12=?    36+12=?    4x12=? 
12x4=? 

2.  How  many  dozen  are  48  ? 

3.  In  12  gallons  there  are quarts. 

4.  In  four  feet  there  are inches. 

5.  At  4  cents  apiece,  what  will  a  dozen  oranges  cost  ? 

6.  What  are  three-fourths  of  forty-eight  ? 

95 

1.  5x8=?      40  +  8=?      6x8=?      7x6=?     42  +  6=? 

2.  6}48  8)48  4)48  12^ 

3.  48  are  how  many  half-dozen  ? 

4.  How  many  8's  in  48  ?     4's?     2's  ? 

5.  How  many  pints  in  6  gallons  ? 

6.  How  many  are  4|^  dozen  ? 

7.  Father  paid  $  9  apiece  for  6  pictures.     Find  the  cost. 

8.  6)42         6)43         6)44         6)50        -6)53        6)54 
9)54         9)55        6)55        9)60        9)62        6)62 


96 


9: 

><5=? 

45  +  9 

9x6=?        6x9='? 


This  represents  a  square  yard. 
1.    How   many   sq.    ft.    in   it  ? 


In   2   sq.    yd.? 
In  5?     In  6? 


In   3?     In   4? 


MULTIPLICATION    AND  DIVISION  41 

97 

1.  Recite  the  table  of  2's,  3's,  4's,  and  5's. 

2.  Recite  the  lO's  to  100. 

3.  Recite  the  ll's  to  99. 

4.  Recite  the  6's  to  6  x  8  and  7's  to  6  x  7. 

5.  Recite  the  8's  to  8  x  6  and  9's  to  5  x  9. 

6.  Recite  the  12's  to  5  x  12. 

7.  Count  4's  from  0  to  48  and  back. 

8.  Count  by  5's  from  0  to  100  and  back. 

9.  Count  by  6's  from  0  to  48  and  back. 
10.  Count  by  3's  from  0  to  48  and  back. 

98 

1.  2x7   3x7   4x7   5x7   6x7   7x6   7x7 

2.  There  are days  in  1  week.      2  weeks  ? 

3.  There  are  42  days  in weeks. 

4.  There  are  49  days  in weeks. 

5.  What  is  one-seventh  of  forty-nine  ? 

6.  2x2    3x3    4x4    5x5    6xQ         1x1 

99 

1.  6x5         6x6         6x7         6x8         48-1-6         6x9 

2.  How  many  half-dozen  in  48  ? 

3.  How  many  half-dozen  in  54  ? 

4.  At  1 6  a  cord,  what  will  9  cords  of  wood  cost  ?  8  cords  ? 


42 


ARITHMETIC   WITHOUT  A  PENCIL 


100 


6x7 

i  of  18 

i  of  54 

8x6 

fof  18 

1  of  54 

6x6 

1  of  36 

I  of  48 

i)  x6 

1  of  36 

fof  48 

7x7 

I  of  49 

f  of  54 

5x7 

f  of  49 

I  of  48 

7x6 

6x9 

5x7 

Multiply : 

101 

1. 

7 

4 

5 

8         7 

9 

6 

6 

7         6 

6 

7 

9 

6         7 

6 

8 

7 

4         8 

2. 

36 -^ 

•6 

49 

■^7 

54-6     42^ 

-7 

45 

-r-9 

42 -i 

'r6     48^8 

3. 

54 -r 

■9 

45 

-i-5 

48-6     49^ 

-7 

36 

-^9 

36  H 

r4     36^3 

4.  Recite  the  6's  from  6  x  6  to  6  x  11. 

5.  Recite  the  9's  to  54. 

6.  Recite  the  4's  and  the  3's. 

7.  How  many  are  9  half-dozen  ? 

8.  In  seven  weeks,  how  many  days  ? 
9»  How  many  dozen  are  six  times  8  ?' 

10.  How  many  working  days  in  7  weeks  ? 

102 


1.  6x7 

2.  49 

±1 

3.  8x7 


7x7 

48 

±^ 
7x8 


5x8 
56-7 


6x8 
56-8 


49-f-7 
8)56 


48+8 
8)59 


7)56         7)57  7)61         7)62 


MULTIPLICATION   AND  DIVISION  43 

4.  At  8  cents  apiece,  what  will  7  copy-books  cost  ? 

5.  If  one  pint  of  berries  costs  seven  cents,  what  do  eight 
pints  cost  ? 

6.  How  many  quarts  in  7  gallons  ? 

7.  How  many  days  in  8  weeks  ? 

8.  Eight  times  seven  is  how  many  more  than  five  times 
eleven  ? 

9.  How  many  desks  in  7  rows,  if  there  are  8  desks  in 
each  row  ? 

10.  I  paid  7  cents  apiece  for  8  balls.     What  did  they  all 
cost  ? 

11.  Seven  times  eight  is  how  many  more  than  six  times 

nine  ? 

103 

1.  ?x?  =  9           ?x?=16  ?x?=25           ?x?=36 
?x?=49          ?x?=64  ?x8  =  56           ?x8  =  64 

2.  64  =  how  many  8's  ?  64  =  how  many  4's  ? 
64  =  how  many  2's?  64  =  how  many  16's  ? 

3.  Eight  times  eight  is  how  many  more  than  six  times 
nine  ? 

•^..  What  is  one-eighth  (|)  of  64  ? 

5.  What  is  I  of  64? 

6.  8  X  8  is  how  many  times  16  ? 

7.  From  8x8  subtract  5  x  12. 

8.  Eight  gallons  are  how  many  pints  ? 

9.  How  many  are  5  dozen  and  4  ? 

10.  At  eight  dollars  a  dozen,  what  will  8  dozen  photo- 
graphs cost? 

11.  Count  by  8's  from  0  to  64  and  back. 

12.  What  is  8x10?     8x11? 


44  ARITHMETIC   WITHOUT  A  PENCIL 

104 

1.  7x10      70-7      7x9      7x8     56  +  7      7x9     9x6 
54  +  9         9x7    10x7     8x7     56^8     9x7      6x9 

2.  Recite  the  7's  to  7  x  9. 

3.  Recite  the  9's  to  9  x  7. 

4.  Eight  times  eight  is  how  many  more  than  seven  times 
nine? 

5.  How  many  are  5  dozen  and  3  ? 

6.  How  many  days  in  9  weeks  ? 

7.  5  doz.  and  3  are  how  many  times  9  ? 

8.  5  doz.  and  4  are  how  many  times  8  ? 

9.  5  doz.  and  3  are  how  many  times  7  ? 

10.  There  are  9  square  feet  in  a  square  yard.     How  many 
square  feet  in  7  sq.  yd.  ? 

11.  At  eight  cents  a  yard,  what  will  9  yards  of  ribbon  cost  ? 

12.  9}63     9)65     9)68     9)70     7}63     7}64     7}69     7)70 

105 

1.  Count  by  6's  from  0  to  72. 

2.  Q6  is  how  many  times  6  ? 

3.  72  is  how  many  times  12  ? 

4.  72  is  how  many  times  6  ? 

5.  How  many  are  6  dozen  ? 

6.  How  many  are  12  half-dozen  ? 

7.  How  many  feet  are  72  inches? 

8.  Recite  the  6's. 

9.  Recite  the  12's  to  12  x  6. 


MULTIPLICATION   AND   DIVISION  45 

10.  What  is  8x10?     Take  one  8  away  and  what  is  left  ? 
Then,  what  is  9  x  8  ?     8x9? 

11.  72  pints  are  how  many  gallons  ? 

12.  Recite  the  8's  to  8  x  11. 

13.  Recite  the  9's  to  9  x  8. 

106 

1.  9x10       90-9       9x9       9x8        72  +  9       9x9 

2.  Count  by  9  from  0  to  99  and  back. 

3.  Recite  the  9's  to  9  x  11. 

4.  6x6         7x7         8x8        9x9 

5.  Add:  99  110  121 

11  11  11 

6.  Count  by  10  from  0  to  120. 

7.  Recite  the  lO's. 

8.  10x11      11x11      12x11      9x9      10x10      11x11 

9.  How  many  cents  in  12  dimes  ? 

10.  How  many  marbles  in  10  dozen  ? 

11.  11  X  11  is  how  many  more  than  10  x  12  ? 

107 

1.  Add: 

72=  ?  xl2        84-  ?  xl2        96=  ?  xl2         132=  ?  xl2 
12  12  12  12 

=  ?  xl2  =  ?  xl2  =  ?  xl2  =  ?  xl2 

2.  Recite  the  7's.     Recite  the  8's.     Recite  the  9's.     Re- 
cite the  12's. 


16 


ARITHMETIC   WITHOUT   A   PENCIL 


3.    Multiply 

: 

6         9 

12 

8 

11 

9         9 

12 

8        7 

11 

7        8 

10 

6 

11 

6         8 

11 

7        9 

9 

8      11 

12 

12 

9 

9       12 

12 

12         9 

12 

8      10 

12 

7 

6 

12        9 
108 

8 

11         S 

_1_ 

2x    2  = 

4x    1  = 

2x    3  = 

2x    4  = 

4x    2  = 

,     , 

.     .  8x 

1  = 

2x    5  = 

2x    6  = 

4x    3  = 

2x    7  = 

2x    8  = 

4x    4  = 

, 

.     .  8x 

2  = 

2x    9  = 

• 

2x10  = 

4x    5  = 

2x11  = 

2x12  = 

4x    6  = 

4x    7  = 

•     • 

.     .  8x 

3  = 

4x    8  = 

, 

.     .  8x 

4  = 

4x    9  = 

4x10  = 

, 

.     .  8x 

5  = 

4x11  = 

4x12  = 

* 

XXX 

00    00    00 

6  = 

7  = 

8  = 

All  products 

even 

numbers. 

8x 

9  = 

8x 

10  = 

8x 

11  = 

8x 

12  = 

MULTIPLICATION   AND   DIVISION  47 

3x    2=     .     .     .     .     .     6x    1= 

3x3=.... 9x1  = 

3x4= 6x2  = 

3x5  = 

3x6= 6x3=       .     .     .     .  9x    2  = 

3x    7  = 

3x8= 6x4  = 

3x9= ^ 9x3  = 

3x10= 6x5  = 

3  X  11  = 

3x12=     .     .     ..     .     6x    Q=       .     .     .     .9x4  = 

6x7=  (9x5=) 

6x    8  = 

6x9=       ....  9  X    6  = 

6x10=  (9x7=) 

6x11  = 

6x12=       ....(9x8=) 

9x    9  = 

Products  of  3's  and  9's  even  and  odd  9  x  10  = 

alternate.      Products  of  6's  all  even.  9  x  11  = 

Notice  peculiarity  of  products  in  9's  :  9  x  12  = 

18,  1  4-  8  =  9  54,  5  4-  4  =  9  90,  9  +  0  =  9 

27,  2  +  7  =  9  63,  6  +  3  =  9  99  =  two  nines 

36,  3  +  6  =  9  72,  7  +  2  =  9  108,  1  +  0  +  8  =  9 

45,  4  +  5  =  9  81,  8  +  1  =  9 


48 


ARITHMETIC   WITHOUT   A   PENCIL 
lip 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

3 

6 

9 

12 

15 

18 

21 

24 

27 

30 

33 

36 

4 

8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

6 

12 

18 

24 

30 

36 

42 

48 

54 

60 

66 

72 

7 

14 

21 

28 

35 

42 

49 

56 

63 

70 

77 

84 

8 

16 

24 

32 

40 

48 

56 

64 

72 

80 

88 

96 

9 

18 

27 

36 

45' 

54 

63 

-  72 

81 

90 

99 

108 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

110 

120 

11 

22 

33 

44 

55 

66 

77 

88 

99 

110 

121 

132 

12 

24 

36 

48 

60 

72 

84 

96 

108 

120 

132 

144 

111 

1.  What  peculiarity  do  the  5's  possess  ? 

2.  What  peculiarity  do  the  lO's  possess  ? 

3.  What  peculiarity  do  the  ll's  possess  ? 

4.  Why  are  the  7's  the  hardest  ? 

5.  How  many  products  to  learn  in  2's  ?     3's  ?     4's  ?    5's  ? 
6's?  7's?     8's?     9's?     lO's?     ll's?     12's? 


MULTIPLICATION   AND  DIVISION  49 

6.  Recite  the  2's,  beginning  at  2  x  2. 

7.  Recite  the  3's,  beginning  at  3x3. 

8.  Recite  the  4's,  beginning  at  4  x  4. 

9.  Recite  the  5's,  beginning  at  5x5, 

10.  Recite  the  6's,  beginning  at  6x6, 

11.  Recite  the  7's,  beginning  at  7  x  7. 

12.  Recite  the  8's,  beginning  at  8  x  8. 

13.  Recite  the  9's,  beginning  at  9  x  9. 

14.  Recite  the  lO's,  beginning  at  10  x  10. 

15.  Recite  the  ll's,  beginning  at  11  x  11. 

16.  Recite  the  12's,  beginning  at  12  x  12. 

17.  How  many  products  in  all  ? 

18.  Which  ones  are  very  easy  ? 

19.  Review  the  hard  ones  daily. 

20.  Write  in  order  all  the  numbers  occurring  in  any  of  the 
tables,  as :  2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  12,  14,  15,  16,  18,  20, 
21,  22,  24,  25,  27,  etc. 

21.  Tell  of  what  numbers  each  is  the  product. 

112 

1.     LIQUID   MEASURE  3.     LONG   MEASURE 

2  pints  make  1  quart.  12  inches         1  foot. 

4  quarts  make  J  gallon.  3  feet  1  yard. 

2.     MONEY  4.     COUNTING 

10  cents         1  dime.  12  things         1  dozen. 

10  dimes        1  dollar.  20  things         1  score. 


50  ARITHMETIC   WITHOUT  A   PENCIL 

5.     TIME 

60  seconds  make  1  minute. 
60  minutes  make  1  hour. 

24  hours  make  1  day. 
.     12  months  make  1  year. 

365  days  make  1  year. 


6.    SQUARES 

2X.2 

3x3 

4x4          5x5 

9x9 

10x10 

11  X  11      12  X  12 

6x6     1x1     8x8 


113 

1.  At  5  cents  a  foot,  what  do  2  yards  braid  cost  ? 

2.  At  24  cents  a  yard,  what  does  1  foot  tape  cost  ? 

3.  If  one  yard  of  rope  costs  10  cents,  what  is  that  per 
foot? 

4.  When  milk  costs  6  cents  per  quart,  what  does  half  a 
gallon  cost? 

5.  What  will  1^  gallons  of  water  cost  at  10  cents  ? 

6.  At  7  cents  a  pint,  what  does  J  quart  wine  cost  ? 

7.  What  will  1  yard  and  1  foot  of  moulding  cost  at  11 
cents  a  foot? 

8.  What  will  1  gallon  and  1  quart  of  milk  cost  at  5  cents 
a  quart? 

9.  12  quarts  of  berries  at  2  cents  a  pint  cost  how  much  ? 

10.  Fanny  went  to  school  every  school  day  but  one  for 
10  weeks.     How  many  days  did  she  go  ? 

11.  Her  brother  went  every  school  day  for  37  days.     How 
many  weeks  did  he  go  ? 

12.  In  a  box  are  72  eggs.     How  many  half-dozen  ? 


/^  MULTIPLICATION   AND  DIVISION  51 

1 13.    How  many  are  2^  dozen  ?     3|  dozen  ? 
1  14.    24  days  are  how  many  weeks  and  days  ? 
j  15.    In  50  days  there  are  how  many  weeks  ? 

16.  Dora  used  24  buttons  on  her  dress.     What  did  they 
cost  at  25  cents  per  dozen  ? 

17.  What  will  48  eggs  cost  at  15  cents  a  dozen  ? 

18.  At  30  cents  a  dozen,  what  will  3  oranges  cost  ? 

19.  How  much  will  a  half-dozen  oranges  cost  at  40  cents  a 
dozen  ? 

20.  I  bought  2 J  dozen  eggs  at  10  cents,  giving  50  cents  in 
payment.     How  much  change  should  the  merchant  give  me  ? 

21.  How  many  inches  in  1  foot  and  9  inches. 

22.  What  will  2  yards  of  lace  cost  at  2  cents  an  inch? 

23.  A  foot  and  a  half  are  how  many  inches  ? 

24.  How  many  inches  in  one-half  yard  ? 

25.  11  pints  are  how  many  more  than  2  gal.? 

26.  John  has  a  dollar  in  his   bank.     The   coins   are  all 
dimes.     How  many  are  there  ? 

27.  How  many  car  fares  will  they  pay  ? 

28.  In  a  certain  box  were  100  oranges.     How  many  were 
left  after  5  dozen  were  taken  out  ? 

29.  Ray  bought  75  cents'  worth  of  paper  and  gave  one 
dollar  in  payment.     What  change  did  he  receive  ? 

30.      52  pints  are  how  many  quarts  ? 

60  pints  are  how  many  quarts  ? 
100  pints  are  how  many  quarts  ? 
100  quarts  are  how  many  gallons  ? 

88  quarts  are  how  many  gallons  ? 

98  quarts  are  how  many  gallons  ? 


52  ARITHMETIC   WITHOUT   A   PENCIL 

31.  James  had  one  dollar  and  he  bought  11  pounds  of  fruit 
at  5  cents  a  pound.     How  much  money  had  he  left  ? 

32.  Four  yards  of  ribbon  at  15  cents  a  yard  cost  

cents. 

33.  Thirteen  yards  of  lace  at  5  cents  a  yard  cost  

cents. 

34.  At  3  cents  a  yard, yards  of  tape  can  be  bought 

for  63  cents. 

35.  QQ  are  how  many  dozen  ? 

36.  How  many  minutes  in  a  quarter  of  an  hour  ? 

37.  One-half  hour  is  how  many  minutes  ? 

38.  It  takes  me  |  of  an  hour  to  walk  a  mile.     How  many 
minutes  is  that  ? 

39.  1^  hours  are  how  many  minutes  ? 

40.  May  had  70  cents  and  spent  l-  dollar.     How  much  had 
she  left  ? 

41.  How  many  score  in  84  ? 

42.  From  100  pints  I  drew  8  gallons.     How  many  pints 
were  left  ? 

43.  96  inches  are  how  many  feet  ? 

44.  96  minutes  are  how  many  more  minutes  than  an  hour  ? 

45.  99  are  how  many  dozen  ?     How  many  score  ? 

46.  At  J  cent  apiece,  what  will  3  apples  cost  ?     5  apples  ? 
11  apples  ?     8  apples  ? 

114 

1.  I  walked  3  miles  an  hour  for  8  hours  on  Monday,  and 
4  miles  an  hour  for  9  hours  on  Tuesday.  How  far  did  I 
walk  in  the  tw^o  days  ? 


MULTIPLICATION  AND  DIVISION  68 

2.  Mr.  Brown  paid  7  dollars  a  head  for  8  calves,  and 
5  dollars  a  head  for  8  sheep.  What  did  he  pay  for  both  ? 
For  which  did  he  pay  more,  and  how  much  ? 

3.  How  much  more  will  9  yards  of  ribbon  at  6  cents 
a  yard  cost  than  11  yards  of  lace  at  5  cents  ? 

4.  I  paid  6  dollars  for  a  hat,  3  dollars  for  a  pair  of  shoes, 
1  dollar  for  a  pair  of  gloves,  ^  dollar  for  a  handkerchief. 
What  did  I  pay  for  all  ? 

5.  Ruby  had  10  dollars.  She  paid  50  cents  for  a  collar, 
50  cents  for  a  ribbon,  75  cents  for  stockings,  25  cents  for  a 
handkerchief,  1  dollar  for  a  par'-a-sol.  How  much  had  she 
left  ? 

6.  A  man  paid  79  dollars  for  a  horse,  and  sold  it  for 
100  dollars.     How  much  did  he  make  ? 

7.  A  man  bought  a  cow  for  81  dollars,  and  sold  her  for 
eight- ninths  of  what  she  cost.     How  much  did  he  lose  ? 

Gain  or  loss  and  how  much  ? 

8.  Bought  for  100  dollars,  sold  for  63  dollars. 

9.  Bought  for  55  cents,  sold  for  a  dollar. 

10.    Bought  12  yards  at  6  cents  a  yard,  sold  it  at  10  cents 
a  yard. 

116 

1.  If  2  pounds  of  candy  cost  10  cents,  what  will  3  pounds 
cost  at  same  rate  ? 

2.  If  there  ^re  12  trees  in  three  equal  rows,  how  many 
are  there  in  two  rows  ? 

3.  Harry  can  read  3  pages  in  30  minutes.  How  long  will 
it  take  him  to  read  5  pages  ? 


54  ARITHMETIC    WITHOUT  A  PENCIL 

4.  Fanny  divided  15  cents  equally  among  three  children. 
How  many  cents  would  she  give  to  7  at  the  same  rate  ? 

5.  Randolph  planted  24  beans  in  8  pots,  putting  the  same 
number  in  each  pot.     How  many  did  he  put  in  3  pots  ? 

6.  Hilda  picks  4  boxes  of  berries  in  20  minutes.  How 
long  will  it  take  her  to  pick  6  boxes  ? 

7.  Mary  makes  9  badges  out  of  a  yard  of  ribbon.  How 
many  inches  of  ribbon  will  be  required  for  4  badges  ? 

8.  Frances  bought  40  sticks  of  candy  for  her  10  guests. 
She  then  invited  4  more  guests.  How  many  more  sticks 
must  she  buy  so  as  to  give  as  many  sticks  to  each  as  she 
planned  to  give  ? 

9.  44  yards  of  carpet  Avere  cut  into  11  equal  strips.  How 
many  yards  were  there  in  9  strips  ? 

10.   If  12  acres  of  land  cost  $600,  what  will  10  acres  cost 
at  the  same  rate  ? 

lie 

1.  If  5  yards  of  calico  cost  20  cents,  how  many  yards  can 
be  bought  for  30  cents  ? 

2.  If  30  sheets  of  paper  will  make  10  kites,  how  many 
kites  can  be  made  from  20  sheets  ? 

3.  If  it  requires  45  loaves  of  bread  to  feed  a  crew  3  days, 
how  many  days  will  60  loaves  feed  them  ? 

4.  I  paid  $3  for  6  theatre  tickets.  How  much  would  5 
have  cost  me  ? 

5.  A  tool  merchant  paid  $44  for  22  rip  saws.  How 
much  would  30  have  cost  at  the  same  rate  ? 

6.  It  required  5  loaves  of  bread  to  make  60  sandwiches. 
How  many  sandwiches  were  made  from  3  loaves  ? 


MULTIPLICATION  AND   DIVISION  65 

7.  If  20  pounds  of  berries  cost  60  cents,  one  dollar  will 
buy  how  many  pounds  ? 

8.  If  a  pasture  will  last  40  sheep  120  days,  how  many 
sheep  will  it  last  80  days  ? 

9.  When  a  6-foot  post  casts  a  shadow  18  feet  long,  how 
long  is  a  pole  that  casts  a  shadow  60  feet  long  ? 

10.    When  it  takes  5  men  12  days  to  do  a  certain  piece  of 
work,  how  many  men  can  do  it  in  10  days  ? 

117 

1.  If  it  takes  6  men  3  days  to  do  a  certain  piece  of  work, 
how  long  would  it  take  2  men  ? 

2.  If  a  stick  2  feet  high  casts  a  shadow  4  feet  long,  how 
long  a  shadow  would  a  post  6  feet  high  cast  at  the  same  time  ? 

3.  If  4  men  dig  28  feet  of  ditch  in  a  certain  time,  how 
many  feet  could  3  men  dig  in  the  same  time  ? 

4.  If  a  railroad  train  travels  90  miles  in  3  hours,  how  far 
will  it  travel  in  5  hours  at  the  same  rate  ? 

5.  A  tailor  used  63  yards  of  cloth  in  making  9  suits. 
How  many  suits  of  the  same  kind  can  he  make  from  84 
yards  ? 

6.  I  used  50  lbs.  of  fruit  in  making  10  quarts  of  jam. 
How  many  pounds  would  be  required  for  6  quarts  ? 

7.  At  40  cents  a  gallon,  what  will  17  quarts  of  syrup 
cost  ? 

8.  At  40  cents  a  gallon,  how  many  pints  of  wine  will 
cost  one  dollar  ? 


56  ARITHMETIC    WITHOUT   A   PENCIL 

118 

1.  At  J  cent  apiece,  what  will  3  apples  cost  ?     5  apples  ? 
11  apples  ?     8  apples  ? 

2.  At  a  half-dollar  apiece,  what  will  12  sailor  hats  cost  ? 
15?     21?     25? 

3.  At  the  rate  of  J  mile  a  minute,  how  far  will  a  train 
go  in  50  minutes  ?     60  minutes  ?     100  minutes  ?     1  hour  ? 

4.  At  the  rate  of  a  mile  in  2  minutes,  how  far  will  a 
train  go  in  J  hour  ? 

5.  At  a  penny  apiece,  how  many  papers  can  I  get  for 
half  a  dollar  ? 

6.  At  a  cent  for  a  half-pint  of  milk,  how  much  will  a 
quart  cost  ? 

7.  At  ^  cent  a  foot,  what  will  1  yard  of  rope  cost  ? 

8.  At  one-half  dollar  a  quart,  what  will  a  gallon  of  wine 
cost  ? 

9.  At  the  rate  of  a  half-pound  a  day,  how  much  sugar 
would  a  family  use  in  one  week  ? 

10.  I  had  100  dollars.  I  put  |^  of  it  in  the  bank.  I  paid 
J  of  what  I  had  left  for  rent.  I  paid  J  of  what  I  then  had 
left  for  bills.     How  much  had  I  after  that  ? 


119 

1.  How  many  cents  are  ^  dollar  ?    J  ?    |  ?    ^?    ^?    ^V  ' 

_3_  ?      _6_  ?       _9_  ? 
10  •        10  •        10  • 

2.  Change  to  inches  : 

1  ft.  10  in.  1  ft.  5  in.  1  ft.  3  in.  3  ft.  6  in. 

1  ft.  7  in.  4  ft.  1  in.  1  ft.  9  in.  5  ft.  7  in. 

1  ft.  11  in.  5  ft.  10  in. 


MULTIPLICATION   AND   DIVISION  67 

IJ  ft.  li  ft.  If  ft.  IJ  ft.  If  ft. 

lift.  If  ft.  IJ^ft.  1/^ft.  111ft. 

3.    Change  to  pints  : 

1  qt.  1  pt.  1  gal.  1  qt.  1  pt.  2  gal.  2  qt.  1  pt. 

1  gal.  1  qt.  2  gal.  1  qt.  1  pt.  1  gal.  1  pt. 

2  gal.  3  qt.               3  qt.  1  pt.  2  gal.  1  qt. 
2  qt.  1  pt.                 2  gal.  1  pt.  2  gal.  3  qt. 

120 

1.  |-  hour  is  how  many  minutes  ?  ^  hour  ?  |  hour  ? 
^  hour  ?     I  hour  ? 

2.  Mary's  mother  said  she  might  stay  3  quarters  of  an 
hour.     How  many  minutes  was  that  ? 

3.  If  it  takes  Dora  a  quarter  of  an  hour  to  walk  to  school, 
at  what  time  must  she  start  so  that  she  may  be  there  5  min- 
utes before  nine  ? 

4.  If  I  can  walk  a  mile  in  half  an  hour,  how  far  can  I 
walk  in  90  min.  ? 

5.  From  nine  o'clock  to  half  past  ten  is  how  many 
minutes  ? 

6.  How  many  minutes  from  quarter  before  11  o'clock  to 
noon  ? 

7.  John  began  to  read  at  half  past  seven  last  evening, 
and  read  three-quarters  of  an  hour.  What  time  was  it  when 
he  stopped  ? 

8.  At  the  rate  of  8  miles  an  hour,  how  far  can  a  boy  ride 
in  30  min.  ?     In  15  min.  ?  45  min.  ? 

9.  At  25  cents  apiece,  how  many  caps  will  cost  $1.25  ? 
10.    At  the  rate  of  10  cents  a  quart,  how  many  quarts  of 

milk   can   be   had   for  $1.44,  and  how  much   change  will 
there  be  ? 


58  ARITHMETIC    WITHOUT   A   PENCIL 

11.  At  10  cents  a  dozen,  what  will  144  buttons  cost  ? 

12.  At  11  cents  a  dozen,  what  will  132  buckles  cost  ? 

13.  At  12  cents  a  dozen,  what  will  108  pins  cost  ? 

14.  At  10  cents  a  foot,  what  will  110  inches  of  moulding 
cost  ? 

15.  At  111  a  head,  what  will  11  calves  cost? 

16.  If  1  ton  of  hay  costs  $12,  what  will  lOJ  tons  cost? 

17.  2)102     3)102     2)104     8)104     3)105     5)105     7)107 

18.  $102  will  buy  3  yards  of  lace  at  how  much  per  yard  ? 

19.  Joe  put  J  of  11.02  in  the  bank.     How  much  did  he 
put  in  the  bank  ? 

20.  How  many  weeks  are  105  days  ? 

21.  104  pints  are  how  many  gallons  ? 

121  ' 

1.  A  man  had  104  bales  of  hay.     He  sold  half  of  it  at  $  1 
a  bale.     What  did  he  get  for  it  ? 

2.  I  bought  ^  of  105  acres  of  land  at  f  2  an  acre.     What 
did  it  cost  me  ? 

3.  John  paid  Jq-  of  flOO  for  a  suit  of  clothes.     What  did 
the  suit  cost  him  ? 

4.  At  the  rate  of  3  for  a  quarter,  how  many  spools  of 
thread  will  cost  11.25? 

5.  I  had  il.09.     I  bought  9  doz.  lemons  at  a  cent  apiece. 
How  much  had  I  left  ? 

6.  Edith  had  11  dozen  seeds.     She  planted  10  seeds  in 
each  one  of  11  boxes.     How  many  had  she  left  ? 

7.  Frank  has  12  rabbits  in  each  of  11  pens  and  two  rab- 
bits besides.     How  many  rabbits  has  he  ? 


MULTIPLICATION   AND  DIVISION  69 

8.  At  5  cents  apiece,  how  many  pencils  can  be  bought 
for  11.05? 

9.  How  many  loaves  of  bread  will  cost  f  1  if  3  loaves 
cost  25  cents  ? 

10.  How  many  quarts  in  104  pints  ? 

11.  2)106  2)108  3)108  4)108  6)108 


9)108    12)108 

2)110 

10)110    11)110 

12.  Subtract : 

- 

120   131   143   140 

138   129 

141   144   132 

108   106   110   106 

108   104 

105   132   129 

122 

1.  A  farmer  has  three  fields  of   54  acres  each.     How 
many  acres  in  the  three  fields  ? 

2.  It  is  54  miles  from  May's  home  to  her  uncle's.     How 
far  is  it  there  and  back  ? 

3.  A  man  divided  $108  equally  among  his  four  sons. 
How  much  did  each  receive  ? 

4.  In  my  orchard  there  are  108  trees  in  6  equal  rows. 
How  many  trees  in  a  row  ? 

5.  How  many  miles  of  iron  car  rails  will  it  take  to  lay 
54  miles  of  track  ? 

6.  A  boy  divided  108  feet  of  kite  string  equally  among 
three  playmates.     How  many  feet  did  he  give  to  each  ? 

7.  106  horses  will  make  how  many  two-horse  teams  ? 

8.  Kate  has  read  half  of  a  book  of  108  pages.     How 
many  pages  has  she  read? 

9.  Mr.  Smith  has  106  acres  of  land.     J  of  it  is  in  orchard. 
How  large  is  his  orchard  ? 


60  ARITHMETIC   WITHOUT   A   PENCIL 

10.  What  will  108  feet  of  rope  cost  at  10  cents  a  yard  ? 

11.  3)111     2)112     7)112     8)112     2)114     3)114     6)114 


5)115  4)111 

5)111 

6)112 

7)113 

8)114 

9)111 

Subtract : 

142  137 

140 

130 

114 

112  : 

L13 

142 

111 

112  111 

114 

112 

99 

38 

77 

59 

79 

12. 

135 

114     

123 

1.  If  it  takes  5  yards  of  cloth  for  one  suit,  how  many 
suits  can  be  made  from  110  yards  ? 

2.  At  10  cents  a  dozen,  how  many  dozen  pens  can  be 
bought  for  11.10? 

3.  At  5  cents  apiece,  how  many  oranges  will  cost  $  1.10  ? 

4.  It  takes  11  feet  of  boards  to  make  a  table.  How 
many  tables  of  the  same  kind  can  be  made  from  110  feet 
of  boards  ? 

5.  If  it  takes  one  man  110  days  to  do  a  piece  of  worlj:, 
how  long  would  it  take  10  men  ? 

6.  If  it  takes  3  men  37  days  to  do  a  piece  of  work,  how 
long  would  it  take  1  man  ? 

7.  If  11  men  do  a  piece  of  work  in  12  days,  how  long 
would  it  take  1  man  to  do  it  ? 

8.  A  baker  divided  111  cookies  among  3  poor  families. 
How  many  did  he  give  to  each  family  ? 

9.  Ill  feet  are  how  many  yards  ? 

10.  J  of  110  minus  J  of  100  =  ? 

11.  12)116    4)116     3)117    9)117    8)117    7)117    6)117 

12.  Subtract : 

120   140   135  140   125  144  121   131   133   151 
116   117   117   116  117   116   59   48   67   98 


MULTIPLICATION   AND  DIVISION  61 

124 

1.  8x7x2x2  =  ?        4x7x2x2  =  ? 

2.  i  56  is  half  of  my  money.     What  is  my  money  ? 

3.  If  a  train  goes  28  miles  an  hour,  how  far  does  it  go  in 
4  hours  ? 

4.  Each  side  of  a  square  field  is  28  rods.     How  many 
rods  around  the  field  ? 

5.  How  many  weeks  are  112  days  ? 

6.  Each  side  of  a  square    field   is  30  rods.      How  far 
around  it  ? 

7.  It  is  100  rods  around  a  certain  square  field,  how  long 
is  one  side  ? 

8.  How  many  weeks  in  114  working  days  ? 

9.  38  yards  are  how  many  feet  ? 

10.  What  will  23  pounds  of  rice  cost  at  5  cents  a  pound  ? 

11.  If  it  takes  4  men  29  days  to  do  a  piece  of  work,  how 
long  will  it  take  one  man  to  do  it  ? 

12.  117  inches  are  how  many  yards  ? 

13.  9x13  =  ? 

14.  It  is  117  feet  around  a  flower  bed  having  3  equal  sides. 
What  is  the  length  of  one  side  ? 

15.  117  and  how  many  are  10  dozen  ? 

125 

1.  2)118     7)119     2)115     7)115     7)119     7)109     7)105 

2.  There  are  118  tons  of  hay  in  two  equal  stacks.     How 
many  tons  in  each  ? 

3.  Miles  traveled  in  France  for  119  days.     How  many 
weeks  was  that  ? 


62 


ARITHMETIC   WITHOUT  A   PENCIL 


4.  118  feet  of  rope  reach  from  the  ground  to  the  top  of  a 
flag  pole  and  back  to  the  ground.     How  high  is  the  pole  ? 

5.  A  man  walks  119  miles  in  a  week.     If  he  walks  the 
same  distance  each  dsij,  how  far  does  he  walk  in  a  day  ? 

6.  2)120    3)120    4)120      5)120    6)120    8)120    11)120 

12)120    7)120    9)120    10)120     7)121     8)121      9)121 

7.  A  certain  street  is  120  feet  wide.     How  many  feet 
from  one  side  to  the  middle  ? 

8.  120  pupils  are  marching  3  abreast.     How  many  in 
each  line  ? 

9.  A  milkman  has  120  quarts  of  milk  in  gallon  cans. 
How  many  cans  does  he  need  ? 

10.  At  a  nickel  apiece stamps  would  cost  $1.20. 

11.  How  many  half-dozen  in  120  units  ? 

12.  Divide  120  into  8  equal  parts.     What  is  one  part  ? 

13.  How  many  dimes  is  $1.20  ? 

14.  120  inches  are  how  many  feet  ? 

15.  There  are  24  hours  in  a  day.     How  many  hours  in  5 
days? 

Change  to  units : 

16.  IJ  dozen     1^ 

17.  3|  dozen     3^ 

18.  ^  dozen       | 

19.  6J  dozen     5J 

20.  if  dozen     3| 

Change  to  dozen  and  units: 

21.  51      42      45      75      100      39      29      49      59      99 


16. 

1^  dozen 

1^  dozen 

1^  dozen 

2J  dozen 

2J  dozen 

17. 

3|  dozen 

S^  dozen 

41  dozen 

5|  dozen 

4i  dozen 

18. 

^  dozen 

1  dozen 

5|  dozen 

3^  dozen 

4|  dozen 

19. 

6J  dozen 

5J  dozen 

7|  dozen 

7|  dozen 

7^  dozen 

20. 

\^  dozen 

3|  dozen 

2lf  dozen 

7|  dozen 

4|  dozen 

MULTIPLICATION   AND  DIVISION  63 

Change  to  dozen : 

22.  18       30      42       66        78       25       37       49       61      73 

23.  How  many  units  in  half  a  dozen  dozen  ?     Q  of  6) 
dozen  ?     Q  of  10)  dozen  ? 

24.  100  -  3  dozen  =  ?     100-6  dozen  =  ?     100  -  5  dozen  =  ? 

25.  100-7  dozen  =  ?     100-4  dozen  =  ?     100-2  dozen = ? 

126 

1.  What  will  ^  dozen  oranges  cost  at  the  rate  of  two 
for  a  dime  ? 

2.  What  will  ^  dozen  eggs  cost  at  20  cents  a  dozen  ? 

3.  What  will  1 J  dozen  lemons  cost  at  the  rate  of  3  dozen 

for  40  cents  ? 

3  dozen  =  40  cents. 

1|  dozen  = cents. 

4.  What  will  9  eggs  cost  at  20  cents  a  dozen  ? 

5.  There  are  2 J  dozen  apples  in  a  certain  box.     What 
are  they  worth  at  2  cents  apiece? 

6.  If  ^  dozen  bananas  cost  10  cents,  what  does  a  dozen 
cost? 

7.  At  the  rate  of  3  for  5  cents,  what  will  a  dozen  oranges 
cost  ? 

8.  At  the  rate  of  3  for  5  cents,  how  many  oranges  can 
be  bought  for  30  cents  ? 

3  oranges  =  5  cents. 
oranges  =  30  cents. 

9.  Jane  had  3  yards  of  ribbon.     She  cut  it  into  two  equal 
pieces.     How  long  was  each  piece  ? 

10.  Mary  found  3  eggs.     What  part  of  a  dozen  did  she 
find? 

11.  6  inches  are  what  part  of  a  foot  ? 


64  ARITHMETIC   WITHOUT   A  PENCIL 

127 

1.  See  if  you  can  divide  any  of  these  numbers  without 
something  remaining :  101,  103,  107,  109. 

2.  Find  all  such  numbers  between  120  and  144. 

3.  At  $  11  a  ton,  what  do  11  tons  of  hay  cost  ? 

4.  132  units  are  how  many  dozen  ? 

5.  What  is  ^  of  1140? 

6.  12  dozen  are  equal  to  how  many  units  ? 

7.  How  many  hours  in  6  days  ? 

8.  A  pound  is  16  ounces.  Two  pounds  are  how  many 
ounces  ?  3  pounds  ?  4  pounds  ?  5  pounds  ?  6  pounds  ? 
7  pounds  ?     8  pounds  ?     9  pounds  ? 

9.  Multiply:        16        16        16        16        16        16        16 

_3        _4        _5         _6         _7        J        _9 

128 

Read  these  numbers: 

1000  1001  1005  1008  1009  1010  1012  1016  1019 

1020  1022  1024  1027  1030  1035  1039  1040  1044 

1050  1057  1060  1061  1067  1070  1078  1080  1083 

1090  1099  1100  1101  1102  1105  1106  1110  1111 

1114  1120  1249  1357  1400  1501  1605  1700  1701 

1754  1781  1895  1903  1958  2000  2100  2107  2111 

2200  2340  2404  2493  2500  2501  2512  2606  2792 

2809  3000  3002  3020  3200  3202  3220  3222  3709 

3789  3904  3940  4000  4100  4010  4270  4705  4809 

4900  5000  5012  6303  6909  7101  7529  8402  8910 

9000  9101  9035  9205  9999  10000  8723  5090  3724 


MULTIPLICATION   AND  DIVISION  65 

Read  these  numbers  and  write  them  from  dictation  : 

11530  10207  12400  12075  11001  9005  11249  12020 

13095  13203  14270  14027  15225  15025  10030  16730 

17025  18009  18888  18400  19500  19050  19005  10950 

20283  21000  22222  23800  24750  25000  40500  29207 

26240  27024  28005  29347  30278  30008  30078  31100 

31750  32041  32007  33445  33275  34475  35550  36405 

37291  38478  39989  40000  40100  41100  41110  42500 

43500  44278  45900  46640  47488  48100  49473  50000 

52251  54785  55290  58707  59005  60200  69583  70750 

74017  60004  81010  31416  25008  30249  67211  60011 

129 

Divide  by  10  :   ' 

200  300  400  500  210  340  480  530  250  330 

460  510  290  370  440  550  240  320  450  590 

970  650  930  350  420  280  660  770  730  800 

1220  1350  1500  1470  1900  1580  1700  1860  1100  1940 

2000  2100  5800  2400  4790  3640  2790  5050  4040  1010 

2020  4270  3480  9360  8080  6230  9490  3270  7440  8880 

Divide  by  10 ;  by  100  : 
5000  3000  9000  3010  4200  7500  8500  7500  9100  9000 
10000  12000  15000  20000  24000  500  600  700  800  900 

130 

Divide  by  20: 

100  300  500  700  900  200  360  580  760  920 
220  400  520  740  940  280  420  600  800  960 
240      440      640      880      980        40        80        60        50        90 

(Divide  in  this  way,  if  easier :  100  =  5  twenties.     300=  3  x  5 
twenties,  or  15  twenties.     60=3  twenties,  360  =  20x18.) 


66                          ARITHMETIC   WITHOUT  A   PENCIL 

Divide  by  30: 

300   330   360  390  270  240  420  450  480  600 

660   630  690  720  750  900  960  990  810  840 

120   150  180  210  510  780  900  930  3000  6000 

Divide  by  40: 

200   400   800  240  280  420  320  360  440  480 

160   820   120  520  640  680  720  620  800  880 

760   840  4000  560  560  600  640  960  2000  8000 

Divide  by  50 : 

100   200   300  400  550  600  700  800  900  1000 

150   250   350  450  500  650  750  850  950  1050 

1500  2000  2500  3000  3500  4500  5000  6000  5500  1200 

Divide  by  100: 

700   900  1100  1300  800  300  1500  2000  500  1300 

1800  2500  2600  1900  1700  1400  2100  3000  3100  3800 


60)360 

60)3600 
80)240 

60)6000 
80)2400 

70)1400 

70)280 

70)7000 

80)8000 

90)3600 

90)810 

90)1800 

60)3000 

80)4800 

60)4800 

131 

(1)  (2) 

quotient 
divisor)  dividend  divisor)  dividend 

quotient 


MULTIPLICATION   AND  DIVISION  67 

(3)  (4) 

divisor)  dividend  (quotient       Dividend  -^  divisor  =  qiiotient. 

No.  1  is  called  short  division.  This  form  should  be  used 
whenever  possible. 

Nos.  2  and  3  are  two  ways  of  writing  long  division. 

No.  4  is  the  form  for  analysis. 

There  is  still  another  way,  which  you  will  use  later.  It  is 
this : 

^^^^^^"^  =  quotient.     —  =  6  which  is  the  same  as  12  h-  2  =  6. 
divisor  2 

132 

Tell  how  many  figures  (besides  remainder)  there  will  be 
in  the  quotient: 


13)1796    14)2049    15)3209    16)1845      17)2748    18)72345 
19)2764    2072109    21)3000    22)39473    13)5429    24)2403 


24)2472    17)183.6    19)1902    18)1965      16)4400    14)3275 

When  a  divisor  of  two  figures  is  not  contained  in  the  first 
two  figures  of  the  dividend,  there  will  be  one  less  place  in 
the  quotient. 

25)19734  26)10345  27)2000  18)T765 

41)40000  32)16732  17)10830  23)^267 


28)20089  121)1229  189)15934  267)2500 


68 


ARITHMETIC    WITHOUT   A   PENCIL 


Dividend 

Divisor 

10634 

15 

19634 

15 

9634 

15 

27395 

27 

20395 

27 

40000 

85 

35000 

35 

16748 

193 

27469 

172 

5349 

158 

133 

Number  of  figures 
in  the  quotient 


134 


How  many  figures  in  the  quotient  ? 
3000  --  25        16000  ^  15 
1758  -^  9         25000  -  374 
1478  -f- 115       14308  -i-  7 
1034  -!-  276       11596  -^  113 
4000  -^  50        12000  -^  300 


59)  7634  ( 
59) 20476  ( 

374) 20476 ( 

893) 89600  ( 
26) 50762  ( 
19) 18032075 ( 

219) 18032075  ( 
49) 593  ( 

273) 1000  ( 
75) 1000  ( 


295378  ^  9 
163842  -  19 
153876  ^  13 
437429  ^  179 
900000  -^  10 


FRACTIONS 

135 

HALVES 

1.  I  had  two  dollars  and  I  spent  one.     What 
part  of  my  money  did  I  spend  ? 

2.  I  had  $4  and  spent  one-half  of  it.     How 
much  did  I  spend  ? 


FRACTIONS  69 

3.  Two  yards  of  silk  cost  1 6.     What  did  one  yard  cost  ? 

4.  There  are  8  pints  in  a  gallon.     How  many  pints  in 
J  gallon  ? 

5.  How  many  cents  in  a  half  dime  ? 

6.  How  many  are  a  half-dozen  eggs  ? 

7.  If  14  marbles  are  divided  between    two   boys,  how 
many  will  each  receive  ? 

8.  il6  was  the  price  of  two  tickets  to  San  Francisco. 
What  was  the  price  of  one  ? 

9.  What  is  one-half  of  eighteen? 

10.    Ten  cents  is  what  part  of  20  cents  ? 

11  12 


of  2  =  ? 

i 

of  14  =  ? 

1  of  20  =  ? 

J  of  18  -  ? 

4 

16 

14 

12 

6 

18 

8 

16 

8 

20 

10 

24 

10 

22 

6 

22 

12 

24 

13 

4 

2 

1  of  26  = 

? 

i 

of  38  =  ? 

28 

40 

30 

42 

32 

44 

34 

46 

36 

48 

14.  Numbers  that  can  be  divided  by  two  without  a  remain- 
der are. called  even  numbers. 

15.  Give  the  even  numbers  from  50  to  60,  and  then  give 
I  of  each. 


70  ARITHMETIC    WITHOUT   A   PENCIL 

16.  Mention  the   numbers   between  60  and  70  that  are 
exactly  divisible  by  2. 

Exactly  divisible  means  that  may  be  divided  without  any 
remainder. 

17.  Give  ^  of  the  even  numbers  from  70  to  80. 

18.  5  is  1^  of  what  number  ?       19.   25  is  J  of  what  number  ? 
6  is  J  of  what  number  ?  24  is  |-  of  what  number  ? 

10  is  I  of  what  number  ?  50  is  |^  of  what  number  ? 

12  is  \  of  what  number  ?  36  is  |^  of  what  number  ? 

20.    2  is  what  part  of  4  ? 

3  is  what  part  of  6  ? 
10  is  what  part  of  20  ? 
50  is  what  part  of  100  ? 

4  is  what  part  of  8  ? 
25  is  what  part  of  50  ? 

21.  If  I  cut  a  pie  into  two  equal  pieces,  each  piece  is  called 
a  half.     There  are,  then,  how  many  halves  in  anything  ? 

22.  Two  halves  of  20  are  how  many  ? 

I  of  10  are  how  many  ?         |  of  24  are  how  many  ? 

23.  1  of  24  ?  36  ?  48  ?  40  ?  72  ?  84  ? 

24.  I  of  each  number  above  ? 

25.  Four  half-dollars  are  how  many  whole  dollars  ?     Six 
half-dollars  ? 

26.  How  many  whole  pages  in  10  half -pages  ? 

27.  Twenty   halves   are    how    many   whole   things?      18 
halves  ?     22  halves  ? 


FRACTIONS  71 

28.  Tell  how  many  whole  things  in  these  :  |-,  ^^  -3^,  -Lon^ 

bJl   40    i  4 

2  '     2  '     2  • 

29.  I  have  five  half-dollars.     How  much  money  have  I  ? 

30.  Joe  has  3  half-dollars.     How  much  money  has  he  ? 

31.  Seven  half-dollars  are  how  much  ? 

32.  Nine  halves  are  how  many  whole  things  and  what 
over  ? 

33.  Change  these  halves  to  whole  things  and  halves  over  : 

I  11      13     JA     11     19     21     2_3     2  5     2  7     2  9 

2*  ~2"'  ~2~"'  ■#■'  "2  '  ~2"'  ~2~'  ^'  ^'     2  '  ^• 

34.  If  you  have  a  dollar  and  a  half,  how  many  half-dollars 
have  you  ? 

35.  !j^  1|^  are  how  many  times  ^  J  ?  ^ 

36.  At  a  half-dollar  a  trip,  how  many  trips  can  you  take 
for  1 1.50?     12.50?     $3.50? 

37.  Change  these  to  half-dollars:  1 4^,  llj,  |10|,  151 
$71. 

38.  Change  to  halves  :  31  9^,  6^,  121,  Hi. 

39.  John  deposited  in  the  bank  at  three  different  times  : 

I I  1 11  and  1 2.     How  much  in  all  ? 

40.  HJ  +  li=-^  21  +  21-1-11  =  ?  2  +  11  +  1  +  1  =  ? 
^  +  ^H  =  ^             ll  +  2Hi=?           HHH2H? 

5J+iHHi-=?  31+21+1+51=? 

41.  Oliver  had  five  dollars  in  the  bank  and  drew  out  $  2 J. 
How  much  had  he  left  ?  What  part  of  his  money  did  he 
draw? 

42.  Lulu  had  1 4.  She  paid  1 21  for  a  pair  of  shoes,  and 
one  dollar  for  a  car  ticket.     How  much  had  she  left  ? 


72  ARITHMETIC   WITHOUT   A   PENCIL 

43.  l-i-i-ll=?  3|-1-1-1=? 

44.  Subtract:   $14.50     110.00     $20.00     $5.00     $25.00 

2.50         4.50       15.50       1.75       17.25 


45.   5x|  =  ?      11  x^: 

6x1  =  ?        3x^  = 
7x1=?      12x1: 


?      4x1=?      2x1=?      1x15=? 
9x1  =  ?     20x1=?      1x25  =  ? 
10x1=?       8x1  =  ?      Jx21  =  ? 


46.  How  much  will  5  presents  cost  at  $^  apiece  ? 

47.  What  will  you  receive  for  picking  12  boxes  of  berries 
at  ^  cent  a  box  ? 

48.  If  it  takes  J  yard  to  make  one  badge,  how  many  yards 
of  ribbon  will  be  needed  for  20  badges  ?  For  25  ?  50  ? 
30?     45? 

49.  A  milkman  has  7  gallon  cans,  each  half  full  of  milk. 
How  many  gallons  of  milk  has  he  ?  . 

50.  Roy  walks  a  half-mile  to  school.  How  far  does  he 
walk  in  19  days  ? 

51.  Half  the  pupils  in  a  certain  class  are  27.  How  many 
in  the  class  ? 

52.  Vane's  father  gave  him  $  5.50,  which  was  half  as  much 
as  Vane  had  earned.     How  much  had  he  then  ? 

53.  If  it  takes  30  minutes  to  go  to  the  post  office,  how 
many  hours  should  it  take  to  go  seven  times  as  far  ? 

54.  Four  pints  are  what  part  of  a  gallon  ? 

55.  In  a  certain  school  of  500  pupils  there  are  261  boys. 
Are  they  more  or  less  than  half  the  school  ? 


ABACTIONS  73 

136 

QUARTERS 

1.  How  many  twenty-five  cent  pieces  make 
a  dollar  ? 

2.  How  many  quarters  in  a  dollar  ? 

3.  How  many  quarters  in  a  lialf-dollar  ? 

4.  How  many  quarters  in  a  dollar  and  a 
half? 

•  5.  A  quarter  of  anything  is  also  called  one-fourth ; 
written,  ^. 

6.  How  many  fourths  in  anything  ? 

7.  Mother  cut  a  cake  into  halves,  and  then  cut  each  half 
into  two  pieces.  How  many  pieces  were  there  then  ?  Each 
piece  was  what  part  of  the  whole  ? 

8.  1=^  1  =  5  1=5  2  =  5 

9-   i=j     ¥=?      10.      3  =  5     20  =  ^      11.    1J  =  5     2-1  =  5 
1  =  1       1  =  5  5  =  5       4  =  5  1|=,     31=5 

1  =  ^        1  =  5  10=5        6=5  1|  =  5      3|  =  5 

1  =  1       1  =  1-  12=5      7  =  5  2|  =  5    4^  =  5 


12.    11=5  21  =  5  31  =  5  41  =  5  5H 


13.  14. 

811+^  i  =  ?  i|+ii=?  l+f+l=?  H  l+i=? 
2H  l=?  iHi|=?  i+i+l='^  H+  i+i=? 
11+  13=?     11+  |=?       i-i-i=?     ii+ii+f='^ 

15.  Selden  has  7  quarters.     How  much  money  has  he  ? 

16.  What  will  10  tops  cost  at  a  quarter  apiece  ? 


74  ARITHMETIC   WITHOUT   A   PENCIL 

17.  Charles  walked  nine  quarters  of  a  mile.  How  many 
miles  was  that  ? 

18.  How  many  apples  were  cut  up  to  make  12  quarters  ? 
20  quarters  ?     16  ? 

19.  Change  these  quarters  to  whole  things  :  |,  -\S  ^--t 
¥,  ^,  ^.  ^,  ^. 

20.  Change  these  quarters  :     J,  -if,  ^,  1^-,  f ,  ^i-,  2f ,  -3^0-. 

21.  What  is  one-fourth  of  20  ?     40  ?     60  ?     80  ?     100  ? 

22.  What  is  I  of  16?    36?    48?    84?   60?   100?   96?   88? 

23.  3  is  J  of  what  ?  5  is  |  of  what  ?  10  is  ^  of  what  ?  20 
is  ^  of  what  ?  25  is  ^  of  what  ?  11  is  J  of  what  ?  T  is  ^  of 
what  ?     9  is  I  of  what  ? 

24.  25  is  what  part  of  100  ?        20  is  what  part  of  80  ? 

1  is  what  part  of      4  ?        80  is  what  part  of  60  ? 
3  is  what  part  of    12  ?        25  is  what  part  of  50  ? 

25.  Tom  had  1 40  in  the  bank.  He  drew  out  1 10.  What 
part  of  his  money  did  he  draw  ? 

26.  Mr.  King  had  5^  pounds  of  venison.  He  gave  away 
^  pound,  ^  pound,  and  |  pound.  How  much  did  he  give 
away  ?     How  much  did  he  keep  ? 

27.  1  quart  is  what  part  of  a  gallon  ?  2  quarts  are  what 
part  of  a  gallon  ?     3  quarts  are  what  part  of  a  gallon  ? 

28.  How  many  quarts  are  there  in  1^  gallons  ?  1 J  gal- 
lons ?     1|  gallons  ? 

29.  A  man  owned  120  acres  of  land.  He  sold  ^  of  it. 
How  many  acres  had  he  left  ? 

30.  My  brother  paid  f  20  for  a  bicycle  and  sold  it  for  |  of 
what  it  cost.     For  what  did  he  sell  it  ? 


FRACTIONS  75 

31.  Fannie  went  to  the  country  for  J  of  a  week.     How 
many  days  was  that  ? 

32.  At  a  quarter  of  a  dollar  apiece,  how  many  melons  will 
cost  12.00? 

33.  How  much  will  a  dozen  25-cent  books  cost  ? 

34.  How  many  oranges  cut  into  quarters  must  I  have  to 
give  one  piece  to  each  of  10  children  ? 

35.  How  many  days  will  it  take  a  boy  to  earn  f  11  if  he 
earns  f  ^  each  day  ? 

36.  What   will  5  pounds  of   candy  cost  at  a  quarter  a 
pound  ? 

37.  lof  32  +  |of  48  =  ? 

38.  (5-2i-i)  +  li  =  ? 

39.  (lof  70)- Q  of  20)  =  ? 

40.  (5  X  I)  —  J  =  how  many  halves  ? 

,137 

EIGHTHS 

1.  If  each  quarter  is  divided  into  2  equal  parts,  how 
many  parts  are  there  in  the  whole  ? 

2.  What  is  each  part  called,  when  there 
are  eight  equal  parts  in  the  whole  ? 

3.  What    are    two    parts    called  ?     Three 
parts?  5?  7? 

4.  How  many  eighths  in  one-half  ? 

5.  How  many  eighths  in  1 J  ?     1^  ? 

6.  Three  quarters  are  how  many  eighths  ? 


76 


ARITHMETIC   WITHOUT   A  PENCIL 


7.  Change  these  to  eighths  :     1,  1^,  If,  IJ,  If,  If,  If, 

1  J,  2,  2f ,  3f ,  51  -V-,  \S  2|,  21,  3|,  5^,  4 J,  41,  5,  1|,  2 J,  GJ,  3|. 

8.  How  many  whole  things  in  these  :     ^-,  ^^-,  -^^^,  -^g*-,  -*^, 

9.  How  many  whole  things  and  eighths  over  in  these  : 

§.¥'¥' ¥.¥'¥'¥? 

10.    Recite  the  multiplication  table  of  8's. 


11.    What  is      12.  What  is      13.  What  is     14.  What  is 

I-  of  96  ? 

I-  of  96  ? 


15. 


17. 


19- 


1  of  24  ? 
I  of  24  ? 
^  of  24  ? 
f  of  24  ? 
I  of  24  ? 
1  of  24  ? 


f  of  24? 
f  of  24  ? 
f  of  24  ? 
f  of  24  ? 
I  of  24  ? 
I  of  24  ? 


^  of  32  ? 

f  of  32  ? 
1  of  40  ? 
I  of  40  ? 
I  of  72  ? 
f  of  96  ? 


1  of  80  ? 
I  of  80  ? 
i  of  48  ? 
I  of  48  ? 


5  is  I  of  what  ? 
4  is  J  of  what  ? 

12  is  I  of  what  ? 
7isi  of  what? 

6  is  1^  of  what  ? 

12  is  what  part  of 
10  is  what  part  of 

4  is  what  part  of 
20  is  what  part  of 

9  is  what  part  of 

12  is  what  part  of 

4  is  what  part  of 
9  is  what  part  of 

10  is  what  part  of 

5  is  what  part  of 


96? 

80? 

32? 

160? 

72? 

96? 
32? 

72? 
80? 
40? 


16.   10 

20 

25 

9 

8 

18.     3 

8 
11 

7 
2 

20.  3 
11 
21 
30 
50 


s  |-  of  what  ? 
s  I  of  what? 
s  ^  of  what  ? 
s  I'  of  what  ? 
s  J  of  what  ? 

s  what  part  of  24  ? 
s  what  part  of  64  ? 
8  what  part  of  88  ? 
s  what  part  of  56  ? 
s  what  part  of  16? 

s  |-  of  what? 
s  1^  of  what  ? 
s  1^  of  what  ? 
s  1^  of  what  ? 
s  ^  of  what  ? 


FRACTIONS  77 

21.  How  many  pints  are  there  in  a  gallon  ? 

22.  1  pint  is  what  part  of  a  gallon  ?  2  pints  are  what  part 
of  a  gallon  ? 

23.  3  pints  are  what  part  of  a  gallon  ?  4  pints  are  what 
part  of  a  gallon  ? 

24.  7  pints  are  what  part  of  a  gallon  ?  5  jjints  are  what 
part  of  a  gallon  ? 

25.  A  grocer  sold  3  pints  from  a  gallon  of  vinegar.  What 
part  of  a  gallon  was  left  ?     What  part  was  sold  ? 

26.  Frank  was  carrying  a  gallon  of  oil.  He  spilled  a  pint. 
What  part  of  a  gallon  remained  in  the  can  ? 

27.  1=^        28.    i-fi=^        29.   i  +  |=^        30.    J-J-H^ 

31.  Mildred  has  $5Q  in  the  bank ;  her  sister  has  |  as  much. 
How  much  has  her  sister  ? 

32.  Our  baby  weighs  12  pounds,  which  is  ^  of  what  I 
weigh.     How  much  do  I  weigh  ? 

33.  PVom  Mary's  home  to  the  sea  is  32  miles.  It  is  ^  as 
far  from  her  home  to  the  mountains.  How  far  is  it  to  the 
mountains  ? 

34.  Ted's  father  raised  160  bushels  of  wheat,  and  |  as 
much  barley.     How  much  barley  did  he  raise  ? 

35.  A  farmer  raised  72  horses  and  sold  f  of  them.  How 
many  did  he  sell? 

36.  Lela  bought  48  yards  of  lace  and  used  |  of  it  on  a 
dress.     How  many  yards  did  she  use  ? 

37.  Lloyd  has  read  15  pages,  which  is  -J  of  the  book.  How 
many  pages  in  the  book  ? 


78  ARITHMETIC    WITHOUT   A   PENCIL 

38.  1  have  read  20  pages  of  a  book  having  160  pages. 
What  part  of  the  book  have  I  read  ? 

39.  After  traveling  |  of  my  journey,  I  have  9  miles  yet  to 
go.     How  many  miles  in  the  whole  journey  ? 

40.  What  part  of  a  whole  day  from  9  o'clock  to  12  ? 

138 
THIRDS 

1.  When  any  whole  thing  is  divided  into  3 
equal  parts,  each  part  is  called  one-third. 

2.  3)15     3)30     3)36     3)12     3)27     3)60 

3.  When  we  divide  a  number  by  3,  we  find 
J  of  it. 

What  is  J  of  15  ? 

10  is  J  of  what  number  ? 

12  is  what  part  of  36  ? 

4.  What  is  ^of  6?  9?  12?  18?  21?  15?  24?  30? 
36?    45? 

5.  8  is  ^  of  what ?  6.  9  is  ^  of  what? 
11  is  ^  of  what  ?  20  is  J  of  what  ? 
15  is  ^  of  what  ?  22  is  J  of  what  ? 

7  is  I-  of  what  ?  12  is  J  of  what  ? 

7.    5  is  what  part  of  15  ? 

10  is  what  part  of  30  ? 

9  is  what  part  of  27  ? 

12  is  what  part  of  36  ? 

8.  How  many  feet  are  there  in  1  yd.  ?  Then  1  ft.  is  what 
part  of  a  yd.?  Two  feet  are  what  part  of  one  yard  ?  3  feet 
are  what  part  of  a  yard  ? 


FRACTIONS  79 

9.    12  inches  are  what  part  of  a  yard  ?     What  part  of  a 
yard  are  24  in.? 

10.  |of6  =  ?  f  of36  =  ?  f  of90  =  ?  |of9  =  ?  fof  24  =  ? 
I  of  99=?  fof  12  =  ? 

11.  I  of  60  =  ?  I  of  66  =  ?  I  of  15  =  ?  f  of  33  =  ? 
I  of  72  =  ?     J  of  21  =  ?     f  of  27  =  ? 

12.  George  had  f  24  in  the  bank  and  drew  J  of  it.  How 
much  did  he  draw  out? 

13.  Cecily  wishes  to  make  9  yards  of  lace.  When  she 
has  made  6  yards,  what  part  of  9  yards  has  she  made? 

14.  Charles  had  a  kite  string  300  feet  long.  He  lost  100 
feet.     What  part  of  the  string  did  he  lose  ? 

15.  A  boy  had  24  newspapers  and  sold  |-  of  them  at  a 
cent  apiece.     How  much  did  he  get  for  them  ? 

16.  It  is  18  miles  to  the  river.  When  you  have  gone  6 
miles  toward  it,  what  part  of  the  distance  have  you  gone  ? 

17.  A  farmer  raised  150  tons  of  hay.  He  sold  50  tons. 
What  part  of  his  crop  did  he  sell  ? 

18.  At  a  cent  apiece,  what  will  J  of  60  oranges  cost  ? 

19.  Find  i  of  75.  -What  is  J  of  150  ?  l  of  60  ?  J  of  54  ? 
J  of  90  ? 

20.  Arthur  had  75  cents,  and  paid  J  of  it  to  go  to  the 
theatre.  How  many  cents  was  that  ?  What  part  of  a  dol- 
lar was  it  ? 

21.  I  had  I  75  and  deposited  J  of  it  in  the  bank.  What 
part  did  I  keep  ? 

22.  Mary  is  ^  as  old  as  her  mother.  If  Mary  is  11,  how 
old  is  her  mother  ? 


80 


) 

ARIG 

DHMETI 

0  wn 

?HOUT 

A   PENCIL 

23.    ^Of 

24. 

J  Of 

25. 

iof 

26. 

J  Of 

27.    iof 

21 

24 

30 

45 

60 

22 

25 

31 

46 

61 

23 

26. 

32 

47 

62 

28.    fof 

29. 

fof 

30. 

fof 

31. 

fof 

32.     1-  of 

75 

36 

240 

180 

50 

60 

27 

270 

330 

100 

45 

21 

300 

360 

200 

139 

NINTHS 

1.  If  each  one-third  be  cut  into  3  equal 
pieces,  how  many  pieces  will  there  be  in  the 
whole  ?  What  is  each  one  of  the  nine  parts 
called  ?     What  are  two  parts  called  ? 

2.  Recite  the  multiplication  table  of  nines. 

3.  18  -f-  9  =  ?        36  -  9  =  ?        90  -  9  =  ? 
54  -  9  =  ?       63  -  9  =  ? 


45  ^  9  =  ? 


4.  What  is  i  of  18?     Of  27?  36?  45?  72?  63?  54?  99? 

5.  6  is  ^  of  what  ?     7  is  |^  of  what  ?     8  is  |  of  what  ? 
9  is  "I  of  what? 

6.  10  is  what  part  of  90  ?     11  of  99  ?     9  is  what  part  of 
81  ?     12  of  108  ? 


7.  If  9  yards  of  ribbon  cost  90  cents,  one  yard  costs 

of  90  cents,  and  two  yards  cost of  90  cents  or cents. 

Three  yards  ? 

8.  If  9  pounds  of  dried  fruit  cost  108  cents,  one  pound 

costs of  108  cents,  and  5  pounds  cost of  108  cents. 

6  pounds  ?     8  pounds  ? 


FRACTIONS 

81 

9. 

What  will  7  milk  cans  hold  if  9  cans  hold  45  gallons  ? 

10. 

f  of  63  =  ? 

11.   1  of  54  =  ? 

12.   1  of  108  =  ? 

^  of  63  =  ? 

A  of  54  -  ? 

1  of  108  =  ? 

13. 

A  of  45  =  ? 

14.   1  of  99  =  ? 

15.    J  of     81  =  ? 

2  of  45  =  ? 

^  of   99  :-  ? 

f  of     81  =  ? 

16. 

1  of  72  =  ? 

17.   A  of  27  =  ? 

18.   f  of  180  =  ? 

1  of  72  =  ? 

f  of  27  =  ? 

f  of  180  =  ? 

19. 

1  of  90  =  ? 

^  of  90  =  ? 

20.  One-third    equals    how    many    ninths  ?     Two-thirds 
equal  how  many  ninths? 

21.  I  =  3.      1=3-       9  =  3-     Find   I  of   any  number  by 
taking  |-  of  it;   find  |  by  taking  |. 

22.  What  is  f  of  18?     Of  27?     Of  36  ?     Of  45?     Of  90? 
Of  54  ?     Of  72  ? 

23.  What  is  f  of  33?     Of  21?     Of  24  ?     Of  30?     Of  42  ? 

Of  48?     Of  60? 

24.  What  is  f  of  9  ?     Of  18  ?     Of  30  ?     Of  27  ?     Of  63  ? 
Of  90  ?     Of  81  ? 

25.  J  +  i  +  i  +  i  =  how  many  ninths  ?     How  many  thirds  ? 

26.  I  +  9  +  9  —  I  =  how  many  ninths  ? 

^'•9  99*         -^         9~"9'         '^         9-  9^9'^9         3 

28.    4  +  |  +  i=?      |-i  =  ?      |-i=?      f-|=? 
29-    l  +  t-i  =  ?       l-f=9.   or  ^.       A  +  J=-? 

30.   J,,i  =  how  many  wholes?     ^f?     Y'     ¥'•     -^'^''     ¥'' 
6  a  9    iii- '? 


82 


ARITHMETIC   WITHOUT   A   PENCIL 


31.  Change  these  ninths  to  wholes ;    -2^,    ^^,    ^g^-,    ■^^,    ■^, 

32.  In  2  whole  things  how  many  ninths  ?     In  3  ?     In  4  ? 
In  10  ?     In  12  ? 

33.  Change  these  wholes  to  ninths :   4,  6,  7,  8,  9,  11,  10, 
5,3. 

34.  9)10.      -V-=H. 

35.  Change  these :    i^,  J/,  ^^  if,  -^f ,  If ^,  ^^,  ^f ,  ^,  M.. 

36.  Change  these  to  ninths:    1|,  If,  1|,  21    2f,  2|,  31, 
3^  101 

37.  1  of  a  farmer's  crop  of  hay  was  10  tons.     What  was 
his  entire  crop  ? 

38.  If  he  sold  ^  of  his  crop,  how  many  tons  did  he  sell  ? 

39.  This  represents  9  sq.  ft.,  or  1  sq.  yd. 

1  sq.  ft.  is  what  part  of   a   square  yard  ? 

2  sq.  ft.  are  what  part  ? 

40.  In  18  sq.  ft.  how  many  square  yards? 

41.  How  many  square  feet  in  3  sq.  yds.  ? 

42.  How  many  square  feet  in  4  sq.  yds.? 

43.  In  33  sq.  ft.  how  many  square  yards  ? 

44.  The  floor  of  my  closet  contains  27  sq.  ft.     How  many 
square  yards  in  it  ? 

45.  The  floor  of  my  bedroom  contains  180  sq.  ft.     How 
many  square  yards  of  carpet  will  cover  it  ? 

46.  The  top  of  mother's  dining  table  contains  36  sq.  ft. 
How  many  square  yards  ? 

47.  A  certain  rug  contains  20  sq.  ft.     How  many  square 
yards  ? 


FRACTIONS 


83 


48.  Another  rug  contains  5  sq.  yd.  How  many  square 
feet  ? 

49.  The  ceiling  of  a  certain  room  contains  5|  sq.  yd. 
How  many  square  feet  ? 

50.  Our  front  porch  was  painted  yesterday.  The  painter 
told  me  it  cost  my  father  $  10.80,  which  was  10  cents  a  square 
foot.     How  many  square  yards  in  it  ? 

51.  Our  sidewalk  has  270  sq.  ft.  of  cement  in  it.  How 
many  square  yards  is  that  ? 

52.  3  sq.  yd.  27  sq.  ft.  are  how  many  square  yards  ? 
18  sq.  ft.  27  sq.  ft.  are  how  many  square  yards  ? 

53.  20  is  what  part  of  180  ?     30  of  270  ?     13  of  117  ? 

54.  40  is  ^  of  what  ?     14  is  |  of  what  ?     15  is  -J  of  what  ? 

140 

SIXTHS  AND  TWELFTHS 


1.  If  one-half  be  divided  into  3  equal  parts,  how  many 
parts  will  there  be  in  the  whole  ?  What  is  one  part  called  ? 
What  are  2  parts  called  ?     3  ?     4  ?     5  ? 

2.  If  each  third  be  divided  into  2  equal  parts,  how  many 
parts  will  there  be  in  the  whole  ?  What  is  one  part  called  '^ 
What  are  4  parts  called  ?     5  ? 

3.  Then  ^  is  how  many  sixths  ?     |-  is  how  many  sixths  ? 


84 


ARITHMETIC   WITHOUT   A  PENCIL 


4. 

1 

= 

S' 

i- 

=  5- 

1  = 

2' 

1 

5. 

+  * 

6. 

= 

? 

1  - 
6  ~ 

i 

-  '6' 

+  i 

i 

+  i  = 

=  6 

i4.i_i_i  —  ?      i_i_i  —  , 

2^3  +  6-^-  3  +  6  —  F- 


I.  Dividing  halves  into  twelfths.  II.  Dividing  sixths  into 
twelfths.  III.  Dividing  fourths  into  twelfths.  IV.  Divid- 
ing thirds  into  twelfths. 


wj  1_ 1_ i_ 

''     2  — 12"        3"~12'        6~12* 


1    _ 


1 1. 


»•     "2^^T2  — 12-       4^^T2~12^-       2        12— 12*       ¥       12— T2- 

1_   1   ___         1 L 

6        12— 12-       S        12  — 12" 


q      l4__l    — I4-JL  — _, 

^'     6  +  12  —  12*        3  +  12  —  1^' 

J.U.     12  — •        12       •        12—-        12  —  - 


11.  The  easiest  way  to  find  -f^  of  any  number  is  to  find 
i  of  it. 

12.  The  easiest  way  to  find  -^^  ^^  ^^^J  number  is  to  find 
1  of  it. 

13.  The  easiest  way  to  find  -^  of  any  number  is  to  find 
i  of  it. 

14.  The  easiest  way  to  find  -^2  ^^  ^^7  number  is  to  find 
1  of  it. 

15.  -^  of     16.  ^2^  of     17.  3^  of     18.  ■^\  of     19.  3^2  of     20.  ^  of 

6  36  40  8  30  9 
12  60  la  44  33  27 
18      30      24      48      21      36 


FRACTIONS 

85 

21.     i^oflO 

22. 

A  Of  40 

23.    ^  of  36 

24.   -J^  of  132 

20 

60 

60 

144 

25 

70 

108 

120 

25.    ^2  of  54 

26. 

A  of  12 

27.   iiof72 

28.   11  of  108 

48 

60 

84 

132 

72 

120 

96 

60 

29.   3^^  of  84 
96 

30. 

-^\  of  108 
132 

31.   1  of  37 
45 

32.  ^2  of    37 
49 

108 

144 

73 

73 

33.  If  four-twelfths  =  J,  eight-twelfths  are  how  many 
thirds  ?     What  is  the  easiest  way  to  find  -^  of  a  number  ? 

34.  Whatis-582  of  30?  36?  48?  60?  108?  96?  84? 
72?     21?     24?     27? 

35.  Since  ■^=*^',  i%  =  |-  What  is  the  easiest  way  to  find 
y^2  of  any  number  ? 

36.  Find  j\  of  24,  16,  40,  96,  44,  60,  36,  48,  20,  12. 

37.  There  are  how  many  12ths  in  J  ?  There  are  how 
many  12ths  in  |  ? 

38.  Find  in  the  easiest  way  \^  of  these  numbers  :  24,  30, 
36,  48,  60. 

39.  There  were  24  blossoms  on  John's  magnolia  tree,  and 
he  picked  -^^  of  them.     How  many  did  he  pick  ? 

40.  How  many  would  he  have  picked  had  he  picked  |-  of 
them?     I?     I? 

41.  The  cook  had  three  dozen  each  of  oranges  and  lemons. 
She  used  |  of  the  oranges  and  -^^  of  the  lemons.  How  many 
of  each  did  she  use  ? 

42.  Suppdse  she  had  used  -I  of  each,  how  many  would  she 
have  used  ? 


86  ARITHMETIC   WITHOUT   A  PENCIL 

43.  If  she  had  used  J  of  the  oranges  and  |  of  tlie  lemons, 
how  many  would  she  have  used  of  each  ? 

44.  A  farmer  raised  48  bushels  each  cf  wheat,  corn,  barley, 
oats,  potatoes,  and  walnuts.  He  sold  ^  of  his  barley,  -J  of 
his  oats,  ^  of  his  potatoes,  and  ^  of  his  walnuts.  How 
many  bushels  of  each  did  he  sell  ? 

45.  The  farmer  raised  60  turkeys,  240  chickens,  and  75 
geese.  He  took  to  market  at  Thanksgiving  ^^2  of  his 
turkeys,  ^  of  his  chickens,  and  ^  of  his  geese.  How  many 
did  he  take  of  each  ? 

46.  A  man  sold  J^  o^  ^^^  land  to  one  man,  ^  to  another,  and 
J  to  another.     What  part  of  all  his  land  had  he  sold  then  ? 

47.  A  boy  bought  18  Suns  and  18  Posts.  He  sold  |^  of  the 
jSuns  and  ^  of  the  Posts.     How  many  did  he  sell  of  each  ? 

48.  I  had  a  box  of  60  oranges  and  gave  away  20.  What 
part  did  I  give  away  ?  How  many  sixths  was  that  ?  How 
many  12ths  ? 

49.  I  ate  6  apples,  which  were  -^^  ^^  ^^^  number  I  bought. 
How  many  did  I  buy  ? 

50.  Roland  sold  9  baskets  of  fruit  this  morning.  This 
was  -^  of  what  he  sold  yesterday.  How  many  baskets  did 
he  sell  yesterday  ? 

51.  -^  of  my  brother's  age  is  6  years.     How  old  is  he  ? 

52.  I  am  ^  as  old.     How  old  am  I  ? 

53.  My  mother  weighs  144  pounds.  I  weigh  -^^  as  much. 
How  much  do  I  weigh  ? 


54.    4f  =  ?      Af=?      il=?      W  =  ? 

¥=?   v-=?   It=? 

55.    53-V  =  ?      3i  =  ^V        10t-V  =  ? 

6i=T2-  %=T2-  m=-' 

10i  =  A-       3J  =  Tj. 

FRACTIONS 


87 


141 


FIFTHS  AND  TENTHS 


1.  Into  how  many  parts  has  any  thing  or 
number  been  divided  if  one  part  is  one-fifth  ? 

2.  If  each  fifth  be  divided  into  two  parts, 
what  will  one  of  the  parts  then  be  called  ? 


3. 

i  -  1  o-       f  = 

lo- 

1 

-  =  TIT-           5  =  TO- 

i-iV=? 

*-tV=? 

4. 

H  —  z  —  To- 

2f 

=  "5"  = 

=  T0-       4-1  =  '^ 

H-tV  =  ? 

5. 

f  +  fo  =  io- 

i  + 

tV  + 

i  =  T0-      |-T0  = 

^   A-i  =  ^ 

6. 

iofl5  =  ?     7. 

iof45  = 

=  ?      8.    |oflO=? 

9.  ^of40  =  ? 

25  =  ? 

55  = 

=  ?                 20  =  ? 

50  =  ? 

85  =  ? 

5= 

=  ?                30  =  ? 

60  =  ? 

10. 

fof30  =  ?    1 

of  45  = 

?    A  of  60  =  ?     f 

3f  40  =  ? 

11. 

■^oi50  =  ?    33_ofl00 

=  ?     ^9_.  of  1000=/ 

^Vof90  =  ? 

12. 

11  is  -^  of  what  ? 

9  is  i  of  what  ?     8  i& 

>  1%  of  what  ? 

12  is 

^^  of  what  ? 

13. 

5  is  what  part 

of  50? 

Of  25  ?     9  is  what  part  of  45  ? 

Of  9C 

I? 

14. 

JoOf|l=? 

15. 

What  part  of  |1 

are  10  cents  ? 

-i  of  1 1  =^  ? 

What  part  of  f  1 

are  20  cents  ? 

Aofll=? 

What  part  of  1 1 

are  50  cents  ? 

f  of  $  1  =  ? 

What  part  of  $  1 

are  90  cents  ? 

lof$l=? 

What  part  of  1 1 

are  70  cents  ? 

f  of  $1=? 

What  part  of  f  1 

are  75  cents  ? 

i^of  .fl  =  ? 

What  part  of  $  1 

are  80  cents  ? 

|of  $1=? 

What  part  of  $  1 

are  60  cents  ? 

^of81=? 

What  part  of  1 1 

are  40  cents  ? 

88  ARITHMETIC   WITHOUT   A   PENCIL 

16.  1  bought  a  bill  of  goods  and  the  merchant  threw  off 
$  2.50,  which  was  -^^  of  the  bill.     What  was  the  bill  ? 

17.  After  paying  |  of  the  price  of  my  bicycle,  I  had  1 10 
yet  to  pay.     What  was  the  cost  of  the  wheel  ? 

18.  I  paid  $  5  for  10  photographs.     How  much  was  that 
apiece  ? 

19.  ^  of  your  money  is  -^^  of  mine.     Your  money  is  $  50. 
What  is  mine  ? 

20.  ^-^  of  your  money  is  ^  of  mine.     My  money  is  $  450. 
What  is  yours  ? 

142 

1.  Here  are  three  ways  of  writing  the  same  example  : 

I  and  II  are  called  Dirision,  as  you  know. 
Ill  is  also  division,  but  we  call  it  a  Fraction. 

I  II  III 

5)10  10^5  =  2  ^-^-^2 

2 

2.  Notice  that  the  dividend  10  is  placed  above  the  line. 
It  is  called  the  nu-mer-a-tor.  The  divisor  is  placed  below 
the  line.  Its  name  is  de-nom-i-na-tor.  (Learn  to  spell  these 
words.) 

3.  Re-write  and  re-read  these  examples  as  fractions  : 
5^2  =  1     1-2=     6-   3=     3h-   6=     5^10=     10-20  = 

12-3=     12-4=     3-^12=     4-12=     3-  9=       5^20  = 

Re-write   and    re-read    these    fractions    as    examples    in 
division : 


FEACTIONS 

4. 

1  =  3+4 

1= 

=  7- 

h8 

f  =  5+ 

S. 

f 

A 

¥ 

6. 

¥ 

¥ 

A 

7. 

U 

t 

!l 

89 


^ 

¥ 

tt 

¥ 

f 

!* 

^5^ 

fl 

A 

f 

f 

¥ 

H 

i 

H 

2 

8.    Re-write   above  examples,   using  the  curved  line  to 
separate  divisor  and  dividend. 

Write  the  following  examples  in  three  different  ways  : 


9 

10 

11 

Divide  16  by    4 
Divide  20  by    5 
Divide  28  by    4 
Divide  30  by  10 
Divide  36  by    9 

Divide  15  by    4 
Divide  20  by    7 
Divide  27  by    9 
Divide  31  by  10 
Divide  35  by    9 

24  divided  by    2 
35  divided  by    6 
33  divided  by  12 
72  divider!  by  12 
80  divided  by  10 

12.   Read  these 

1^'    9^  h   12'  ^'1'  P 

h  tV'  Te- 

as 

examples  in  division  :    f ,  \S  i^^  |.  ^g-, 

ii^  ¥'  tV  ¥'  ¥'  {h  ¥.  ¥'  ¥'  ¥'  i' 

13.  Tell  which  is  the  denominator,  or  divisor,  in  each 
fraction  in  Nos.  4,  5,  6,  7,  and  12. 

14.  Tell  which  is  the  numerator,  or  dividend,  in  the  same. 

15.  Select  all  the  fractions  in  Nos.  4,  5,  6,  7,  and  12  having 
the  denominator  larger  than  the  numerator. 

16.  These  fractions  are  called  proper  fractions.  Read 
thoughtfully  now,  and  you  will  understand  why.  You  have 
seen  that  a  fraction  is  really  an  example  in  division.  When 
we  divide  any  thing  or  number,  we  take  part  of  it.  You 
know  that  we  usually  speak  of  a  part  of  anything  as  mean- 
ing less  than  the  whole,  as  :  Give  me  part  of  your  orange  ; 
He  sold  part  of  his  farm.     Therefore,  those  fractions  that 


90  ARITHMETIC    WITHOUT   A   PENCIL 

are  less  than  one  whole  thing,  or  unit,  are,  properly  speaking, 
fractions,  and  we  call  them,  proper  fractions.  (If  you  do  not 
understand  this,  read  again.)  Which  of  these  are  proper 
fractions  :     J^,  \^  -^,  ^,-,  J^,  i^,  ^\  ^,  |  ? 

17.  Go  over  Nos.  4,  5,  6,  and  7  again  and  select  the  i^roper 
fractions. 

18.  Make  twenty  proper  fractions. 

19.  Now,  fractions  that  represent  a  whole  thing  or  more 
than  a  whole  thing  are  also  fractions,  for  they  indicate  or 
show  division ;  so  we  call  them  im-proper  fractions.  {Im 
means  not.,  as  :  im-pure.,  im-modest.^ 

20.  Select  the  improper  fractions  in  Nos.  4,  5,  6,  7,  and  12. 

21.  Make  twenty  more  improper  fractions. 

143 

1.  Change  these  improper  fractions  to  whole  numbers: 

JL5.    lA    11    21     2JL    Ali.   10     3  0     3Q.    3-g.     3_6.    ^6.   3A   ^6-     3fi_     3  6     3  5. 
#'  "#'     3  '  "T"'     9  '     3  '  10'  "5"'  "6  -'     2^'  -#'     1  '  •  6  '     9  '    12'  T^'  " 5  ' 

¥2A     2  4      %A.     %A     2__5_    A3     6_4     _8_1     IJLS.     ^4      9  6.    _L3  2      lj2JL    JL4_4_ 
'    12'  "F  '   "3  '  "2  '   "5  '     7  '     8  '     9  '     12  '    12'    12'     12  '     11  '     12  ' 
180     2  00     U)  0  0     _1_0_0  0     1000     10  0,0    ^J)_0.    M^     50  jl    iJLO     5.00.     100 
2  0"'  TOO'     S'OTT'     2  00'       2^'       5     '    50  '   10  0'  ^    '    2  5  '     1    '      1^' 
100     JJLQ.    8.15     600     £.2  5. 
TT^'     20'   it^'   1^17'    12  5- 

2.  When  a  whole  number  and  a  fraction  are  used  together 
to  make  one  number,  the  number  is  called  a  mixed  number, 

r,s5  .     1  1      91      Q2 


3-  H=l 

4.  7i= 

5-  4=* 

6.  8f  = 

7.  li= 

8.  21- 

n= 

10|= 

lf  = 

54= 

1|  = 

6i= 

H= 

121  = 

2*= 

10|= 

1|= 

7|= 

4J= 

20^  = 

2f= 

334= 

H  = 

8|= 

6J= 

25  J = 

34= 

40|= 

2|  = 

12|= 

FRACTIONS  91 

9.  Change  4|  to  an  improper  fraction.  Since  in  1  there 
are  5  fifths,  in  4  there  are  4x5  fifths,  or  20  fifths,  plus  2 
lifths,  are  22  fifths,  written  ^-. 

Analyze : 

10.  3|  are  how  many  fifths  ? 

11.  7|^  are  how  many  fifths  ? 

12.  8|^  are  how  many  sixths  ? 

13.  9J  are  how  many  sixths  ? 

14.  4|-  are  how  many  sevenths  ? 

15.  5|^  are  how  many  sevenths  ? 

16.  9|-  are  how  many  eighths  ? 

17.  4^  are  how  many  ninths  ? 

18.  7|  are  how  many  ninths  ? 

19.  5^  are  how  many  tenths  ? 

20.  7^Q  are  how  many  tenths  ? 

21.  8|^  are  how  many  sevenths  ? 

Reduce  (change)  to  improper  fractions  : 


22.  lOf 

23.  5i| 

24.  7f 

25.  8f 

26.  7| 

27.  30| 

28.  121 

H 

llf 

\^ 

41^ 

12tV 

10| 

6i 

20f 

501 

n 

8| 

21i 

50J 

14f 

lOf 

12A 

28f 

50|: 

161 

33i 

6f 

29.  Do  you  see  that,  in  changing  a  mixed  number  to  an 
improper  fraction,  the  denominator  remains  the  same  ?  Do 
you  see  that  we  get  the  new  numerator  by  multiplying  the 
denominator  by  the  whole  number  and  then  adding  the 
numerator  ?  As :  5^  are  how  many  twelfths  ?  5x12 
twelfths  are  60  twelfths,  plus  11  twelfths,  are  71  twelfths,  ^. 

'^1%  =  tV-         7  X  10,  +  3  =  73.     Therefore,  7^  =  ^. 


92  ARITHMETIC   WITHOUT   A   PENCIL 

30.  Change  these  mixed  numbers  to  improper  fractions  as 
explained  in  No.  29 : 

2^VC2  xl3,  +3- numerator.)     1^^,  4^,  2^-^,  2lf,  3^, 
5A'  4A,  Hh  43V  l^s'  123V,  l\h  2A.  5^,  30|,  15|,  1-if ,  9i. 

31.  Change  these  mixed  numbers  to  improper  fractions  : 


H 

6| 

3* 

8| 

6f 

3f 

H 

H 

n 

8i 

61 

5* 

8A 

4| 

H 

H 

8| 

8| 

H 

6| 

7* 

^ 

n 

2f 

8? 

6| 

32.    Change  these  improper  fractions  to  whole  or  mixed 
numbers.     (Remember  they  are  examples  in  division.) 

lA    13.    _24    M.    5J.    ID.     4  9.     _20    3^    _3  2     33      2JL   _2J1    _2  7     3  4     4  0 
T")     3  »     a  '     8  '    10'    12'    12'      3  '     3  '     i  '    ^'     9  '    7  '      8  '   11'    11' 

44     18     1_2JL    120,    lAA.    11     lA     9A    M,     90     lj)_a     IJLQ.     IJLQ.     1_2_A 
11'    11'     11'     11'     12'    iTT'    10'    10'    10'    11'     12'     11'     20'     20' 

JL5JI    1_5_3.    10_0 

T^O  '  ^0  '      9^*  ^ 

144 


1.  What  is  a  fraction  ?    The  number  below  the  line  is  the 

.     The  number  above  the^  line  is  the .     These  are 

called  the  terms  of  the  fraction.      The is  the  divisor. 

The is  the  dividend. 

2.  What  is  a  proper  fraction?      What  is  an  improper 
fraction  ? 

3.  What  is  a  mixed  number  ? 

4.  Another  name  for  whole  number  is  integer.     Use  integer 
hereafter. 

How  do  you  change  an  improper  fraction  to  an  integer  or 
mixed  number  ? 

5.  How  do  you  change  a  mixed  number  to  an  improper 
fraction  ? 


FRACTIONS  93 

6.  Write  10  integers  that  can  be  divided  by  2  without  a 
remainder. 

Let  us  write  this  in  another  way  that  means  just  the  same  : 
Write  10  integers  exactly  divisible  by  2.  Use  these  new 
words  hereafter. 

7.  Give  all  the  numbers  between  20  and  50  that  are  exactly 
divisible  by  2.     Between  80  and  100. 

8.  Numbers  exactly  divisible  by  2  are  called  even  numbers. 
Give  the  even  numbers  from  50  to  70. 

9.  Give  the  numbers  below  30  that  are  not  even. 

10.  All  numbers  not  even  are  odd. 
Give  the  odd  numbers  from  30  to  60. 

11.  Give  the  numbers  to  36  that  are  exactly  divisible  by  3. 

12.  I  wish  to  use  another  word  which  may  be  new  to  you. 
It  is  digit.  The  number  12  has  two  digits,  1  and  2.  15  has 
two  digits,  1  and  5. 

13.  Notice  the  numbers  you  gave  in  No.  11  :  3,  6,  9,  12, 
15,  18,  21,  24,  27,  30,  33,  and  36.  Notice  that  the  sum  of 
the  digits  in  the  number  12  (1  +  2  =  3)  is  exactly  divisible 
by  3.  15  (1  +  5  =  6),  18  (1  +  8  =  9).  Is  it  true  of  21,  24, 
27,  and  the  others  ? 

14.  It  is  true  of  all  numbers,  however  large,  that  if  the  sum 
of  the  digits  be  exactly  divisible  by  3,  the  number  is  exactly 
divisible  by  3. 

Tell  by  the  test  given  above,  which  of  these  numbers  are 
exactly  divisible  by  3  :  39,  60,  120,  150,  312,  453,  762,  513, 
75,  705,  7005,  111. 

15.  Make  ten  more  numbers  exactly  divisible  by  3. 

16.  Give  the  numbers  from  36  to  72  that  are  exactly 
divisible  by  3. 


94  ARITHMETIC   WITHOUT   A   PENCIL 

17.  What  is  an  integer  ?     What  is  a  digit  ? 

18.  What  does  exactly  divisible  mean  ? 

19.  What  are  even  numbers  ?     What  are  odd  numbers  ? 

20.  What  numbers  are  exactly  divisible  by  2  ? 

21.  Describe  numbers  exactly  divisible  by  3. 

145 

1.  Here  is  another  new  word.  A  number  that  will  exactly 
divide  another  number  is  called  a  factor  of  that  number. 

2.  Give  a  factor  of  6.  Another.  Give  a  factor  of  9. 
Of  14.  Of  21.  Give  five  factors  of  12,  six  factors  of  24,  six 
of  36,  seven  of  48,  four  of  50. 

3.  The  factors  that,  multiplied  together,  will  produce  a 
given  number  are  called  a  set  of  factors,  as  :  one  set  of  factors 
of  12  is  3  and  4,  another  set  of  factors  is  2  and  6. 

4.  Give  two  sets  of  factors  of  18.  Give  three  sets  of 
factors  of  24. 

5.  Give  three  sets  of  factors  of  30.  Give  three  sets  of 
factors  of  100. 

6.  Give  all  the  sets  of  two  factors  of  these  numbers :  32, 
35,  60,  64,  21,  28,  48,  3Q, 

7.  Give  five  numbers  that  have  2  for  one  factor. 

8.  Give  five  that  have  2  and  3  and  another. 

9.  Give  five  that  have  5  for  one  factor. 

10.  All  numbers  that  contain  5  as  a  factor  end  in  either  — 
or  — .     All  numbers  having  the  factor  10  end  in . 

11.  Give  ten  numbers  containing  9  as  a  factor.  Add  the 
digits  composing  each  of  the  numbers,  and  you  will  see  that 
each  sum  is  exactly  divisible  by  9.  This  is  true  of  all 
numbers  divisible  by  9. 


FRACTIONS  95 

12.  Tell  by  looking  at  these  numbers  which  are  exactly 
divisible  by  9  :  342,  217,  81,  103,  801,  810,  108,  180,  54, 
504,  405,  540,  450,  700,  702,  315,  245,  713,  711. 

13.  Make  ten  more  numbers  exactly  divisible  by  9. 

14.  Numbers  like  1,  2,  3,  5,  11,  13,  that  have  no  factors 
but  themselves  and  1,  are  called  prime  numbers.  So  here 
you  have  another  new  word.  Give  the  prime  numbers  from 
13  to  30.  Give  the  prime  numbers  from  20  to  40.  From  40 
to  50.     From  50  to  75,  75  to  100. 

15.  In  deciding  whether  or  not  a  number  is  prime,  you 
must  examine  it  with  care.  There  are  many  more  that  are 
not  prime  than  there  are  prime.  Those  that  are  not  prime 
are  called  com-pos-ite. 

16.  Give  the  composite  numbers  below  25.  Below  50. 
Below  75.     Below  100. 

17.  Give  prime  factors  of  these  numbers  : 

4  =  2,2      9  =  3,3      14  =  2,7      18  =  2,3,3      22  =  2,11      26 
6  10  .15  20  24  27 

8  12  16  21  25  28 

18.  Give  prime  factors  of  :  30,  32,  33,  34,  35,  36,  38,  39, 
40,  42,  44,  45. 

19.'  Give  prime  factors  of  each  composite  number  from  45 
to  55. 

20.  Give  the  prime  factors  of  the  next  10  composite  num- 
bers above  55. 

21.  Give  prime  factors  of  70,  71,  72,  73,  74,  75,  76,  77,  78, 
79,  80. 

22.  You  should  make  yourself  very  familiar  with  factors. 
Go  on  with  numbers  to  100  or  farther  if  you  can. 


96  ARITHMETIC    WITHOUT   A   PENCIL 

146 

1.  What  is  a  factor  ? 

2.  What  is  a  prime  number  ?     What  is  a  prime  factor  ? 

3.  What  is  a  composite  number  ?  How  many  prime 
numbers  are  there  below  100  ? 

4.  Describe  numbers  exactly  divisible  by  5.     By  3.     By 

9.  Use  2,  5,  and  3  as  factors  ;  as  digits.     Use  3,  3,  and  5  as 
factors ;  as  digits. 

5.  What  factor  is  found  in  both  10  and  15  ?  12  and  15  ? 
21  and  35  ?  A  factor  that  is  found  in  each  one  of  two  or 
more  numbers  is  said  to  be  a  common  factor  of  those  numbers. 

6.  Give  a  common  factor  of  : 

12,  24,  and  36.  21,  28,  and  35.  16  and  20. 

15,  25,  and  30.  18,  21,  and  24.  20  and  24. 

7.  Give  the  largest  number  that  is  a  common  factor  in 
the  sets  of  numbers  above.  Such  a  factor  is  called  the 
greatest  common  factor^  written  g.  c.  f.,  or  sometimes  g.  c.  d., 
meaning,  greatest  common  divisor. 

8.  g.  c.  f.  of  18,  27,  36  9.  g.  c.  f.  of  35,  42,  49 

10.  g.  c.  f.  of  30,  60,  70  11.  g.  c.  f.  of  ^^,  %b,  95 
12.  g.  c.  f .  of  33,  m,  88  13.  g.  c.  f .  of  108,  132,  144 
14.  g.  c.  f.  of  25,  50,  75,  100  15.  g.  c.  f.  of  40,  60,  80,  100 
16.  g.  c.  f.  of  54,  63,  81,  99  17.  g.  c.  f.  of  15,  30,  60,  75 
18.  g.  c.  f.  of  17  and  51  19.  g.  c.  f.  of  14  and  42 

20.  g.  c.  f.  of  30  and  41  21.  g.  c.  f.  of  18  and  24 
22.  g.  c.  f.  of  19  and  38  23.  g.  c.  f.  of  9  and  11 
24.  g.  c.  f.  of  16  and  78     25.  g.  c.  f.  of  15  and  21 


FRACTIONS  91 

26.  g.  c.  f.  of  16  and  27  27.  g.  c.  f.  of  14  and  28 

28.  g.  c.  f.  of  16  and  48  29.  g.  c.  f.  of  13  and  17 

30.  g.  c.  f.  of  21  and  27  3i.  g.  c.  f.  oi  21  and  24 

32.  g.  c.  f.  of  21  and  28  33.  g.  c.  f.  of  21  and  29 

34.  g.  c.  f.  of  21  and  81  35.  g.  c.  f.  of  13  and  117 

147 

1.  What  are  the  terms  of  a  fraction  ? 

2.  What  is  a  common  factor  ? 

3.  What  is  the  greatest  common  factor  of  two  or  more 
numbers  ? 

4.  Does  changing  f  to  |-  change  the  value  of  the  fraction  ? 
Is  I  of  an  apple  just  as  much  as  |-  of  an  apple  ?  Will  ^  of  a 
dollar  buy  as  much  as  |  of  a  dollar  ? 

5.  This  changing  the  terms  of  a  fraction  to  smaller  num- 
bers without  changing  the  value  of  the  fraction,  is  called 
changing  to  lower  or  to  lowest  terms. 

6.  Change  these  fractions  to  their  lowest  terms  by  divid- 
ing both  terms  by  their  greatest  common  factor : 

^    ^    is    j%    fi    u    ^    a    ^    i! 

f     A     A     A     A     A     if     M     M     if 
A     A     if     A     A     A     A     41     U     U 

i.         S-         Xi  X-         -K-         -9-         2.1         %Sl         1.1         4£ 

9  12  15  2¥  2¥  36  36  30  30  80 

7.  Change  to  lowest  terras:    ff,  ff,  ff,  ^|,  if,  if,  |f, 

if'  ft.  ff  H'  H-  M'  T%.  If.  1%.  1%.  If.  II.  If.  M. 
**■  iff.  ill.  iff.  iff.  iff.  if.  ft.  T^F.  If.  If.  ff.  ^P 
^.  If.  If.  If.  If.  If.  ff.  T^.  iff.  m- 


98  ARITHMETIC   WITHOUT   A  PENCIL 

8.  Read  g.  c.  f. 

13,  26,  39        39,  42  99,  121,  110        49,  63,  84 

28,  42  50,  75,  100        111,  121,  132        54,  90,  120 

9.  Reduce  to  lowest  terms:  ||,  ff,   if,  f|,  ff,  ff  ffj, 

JLA.      1-a  •    49       6  3       A 4    'Jl±_      _5_4_      _9JL      110       3  9      15       lA      15. 
100'    -63'    ¥T'     84'     90'     120'     108'     120'     12  1'    ¥0'     1^'    65'    ^0' 

TOlT'    51'    ^y    "5  6'    6T'    9  6'    "5  4'    76'    YS'    3  9'    tI'    tA'    tA* 

10.  Make  five  fractions  which  you  reduce  to  lowest  terms 
by  dividing  both  terms  by  12. 

11.  Make  5  fractions,  the  g.  c.  f.  of  whose  numerator  and 
denominator  is  6. 

12.  When  are  fractions  in  their  lowest  terms  ? 

148 

1.  I  have  two  pieces  of  land  containing  respectively  56 
and  64  acres.  What  is  the  largest-sized  lot  into  which  I  can 
divide  these  two  pieces  and  have  the  lots  of  uniform  size  ? 

2.  A  farmer  has  72  bushels  of  oats,  96  bushels  of  barley, 
60  bushels  of  corn,  and  108  bushels  of  wheat.  He  wishes  to 
put  his  grain  in  bins  of  uniform  size.  What  is  the  largest- 
sized  bin  that  will  enable  him  to  do  this  ? 

3.  A  merchant  has  three  pieces  of  silk  containing  respec- 
tively 14  yards,  35  yards,  and  84  yards.  He  wishes  to  cut 
them  into  uniform  lengths.  What  is  the  longest  possible 
length  ? 

4.  A  grocer  has  50  lbs.  of  rice  and  72  lbs.  of  tapioca.  He 
wishes  to  put  them  in  equal  parcels.  What  is  the  largest- 
sized  parcel  into  which  he  may  put  them  ? 

5.  An  orchardist  has  27  lemon  and  36  orange  trees  to 
plant.  How  many  trees  must  he  put  in  a  row  so  that  he  will 
have  the  same  number  of  rows  of  each  ? 


FBACTIONS 


99 


149 

1.    It   is   often   necessary  to    change  fractions  to  higher 
terms. 


1  —  2 
2—? 


1  —  2 
3  —  6 


2  =  _4^ 
6        12 


i  —  ^-u     |— A 


You  see  this  can  be  done  without  changing  the  value  of 
the  fractions.  When  we  changed  to  lower  terms,  we  were 
careful  to  divide  both  numerator  and  denominator  by  the 
same  number. 

When  we  change  to  higher  terms,  we  must  be  careful  to 
multiple/  both  numerator  and  denominator  by  the  same  num- 
ber, so  as  not  to  change  the  value  of  the  fraction. 

2.    Change  to  twelfths  : 


fx|  =  T%             i  =  T2             i  =  l2 

f— 12         i'- 

-T2           f=T2 

3.    Change : 

1  to  ninths        ^  to  fifteenths 

f  to  fifteenths 

^  to  tenths 

1  to  tenths        |  to  fifteenths 

1  to  20ths 

1  to  25ths 

1  to  SOths          1  to  24ths 

1  to  24ths 

f  to  24ths 

f  to  24ths       ^  to  24ths 

1  to  24ths 

f  to  21sts 

4.    Change ; 

f  and  f  to  twelfths       J  and  | 

to  twelfths      f 

and  ^  to  18ths 

i  and  f  to  18ths            f  and  | 

to  20ths          ^ 

and  J  to  12ths 

5.  Changing  two  or  more  fractions  to  other  fractions,  all 
of  which  have  the  same  denominator,  is  called  changing  to 
common  denominator,  and  we  usually  wish  to  change  to  the 
least  common  denominator.  To  do  this  well,  we  need  to 
study  least  common  multiple. 

Now,  the  least  common  multiple  of  two  or  more  numbers 
is  the  smallest  number  that  will  exactly  contain  each  of  them. 


100  ARITHMETIC   WITHOUT   A   PENCIL 

.  6.  What  is  the  least  common  multiple  of  2  and  4  ?  2  and 
3  ?  2  and  5  ?  5  and  10  ?  3  and  4  ?  3  and  5  ?  3  and  6  ? 
3  and  18  ?     7  and  14  ?     15  and  5  ?     8  and  3  ?     24  and  8  ? 

7.  Change  these  fractions  to  fractions  having  the  least 
common  denominator: 

J  and  I     ^  and  |-      |  and  |       |  and  -^^^     |  and  |     |  and  | 
I  and  f     i  and  -^^     f  and  -\    -If  and  |      f  and  f     1  and  i 

8.  Give  the  1.  c.  m.  of : 

2,  4,  6  4,  6,  8  6,  9,  12  6,  12,  14  6,  12,  15 

15,  21  18,  21  6,  12,  24        18,  54  4,  6,  8,  12 

9.  Reduce   to   fractions   having    the    least    common    de- 
nominator : 

¥  and   9  tV  ^i^d  6  12  and  4  tV  and  J^  and  | 

A  and  f  -jV  and  f  |  and  -^\  j\  and   ^  and  f 

I   and  ^  f  and  |-  |   and   |  |-  and  |^  and  | 

^  and  f  /:j  and  f  -^^  and  |  -^^  and  |  and  f 

•|  and  I"  ^^  and  ^  '  ^  and  |^  ^  and  y^g  and  ^ 

150 

1.  3  sixths  plus  two  sixths  are  how  many  sixths  ? 

2.  2  fourths  plus  1  fourth  are  how  many  4ths  ? 

3.  4  twelfths  and  3  twelfths  are  how  many  twelfths  ? 

4.  5  tenths  and  2  tenths  are  how  many  lOths  ? 

5.  5  fifteenths  plus  three  15ths  are  how  many  15ths  ? 

A+Jj=?  A+j't=?  A+A=?  A+A=?  A+H=? 


FRACTIONS  101 

Change  to  least  common  denominator  and  add : 


7. 

hi 

hi 

i'i 

hi 

hi 

hi 

hi 

h  i 

8. 

hi 

hi 

hi 

hi 

hi 

hi 

hi 

h  i 

9. 

hi 

hi 

I'i 

hi 

hi 

tV'4 

^^i 

hi. 

10. 

i+f 

HI 

i+l 

i+l 

i+i 

i+i 

I+I 

Hi 

11-  Hi  Hi  Hi  Hi  I+I  i+A  f,+i  Hi 
"•  H+i+f  ^5+l+f  HHi  l+i^+/tr  iHI+l 
13-  f+f    ^V+l    l+f    f+A    l+f    1+1    HHi 

"•    f  +  f     A  +  i     f  +  l     f  +  1      l  +  f     T\  +  i       l+f+i 

15-  f+l  l+f  t  +  f  t  +  f  t  +  l  I  +  I  f+f+i 
".  Hi  I+I  l+f  I+i  Hi  ^+i  A+A+i 
"•  A+l  f+iV  i+l  i+iV  A+i  f+f  tV+I+1 

18-  i  +  i  +  i     1+2^  +  J      f+l  +  f      l+l+i     Hi  +  i 

19-  l+Hf    f+i+J     i+i+iV   HiV+i    l+f+i 

20.  i+r+l    i+f+i   A+HJ     l+l+f    l+f+i 

21.  i+j+i+j^   2  +  x+i+j^  Hi+i+i  i+i+i+i 

22.  f  +  i  +  i  +  A      i  +  Ki  +  T^      Vs  +  ^  +  i^  +  f 

23.  A+A  yV+I  -M+I  H+41  M+A  tVj+A 
2*.  1%+A  H+iV  t\+*  tIt+I    A+A     I+tIo 

151 

1.  A  boy  spent  J  of  a  dollar  for  a  top,  ^  of  a  dollar  for 
paper,  and  f  ^  for  a  ball.     What  did  he  spend  for  all  ? 

2.  A  farmer  sold  one-half  of  his  crop  to  one  man  and  f  to 
another.     What  part  of  his  crop  did  he  sell  to  the  two  men  ? 

3.  Joel  studied  his  spelling  J  of  an  hour  and  his  music 
I  of  an  hour.     How  long  did  he  spend  studying  both  ? 


102  ARITHMETIC   WITHOUT   A  PENCIL 

4.  A  father  willed  |  of  his  property  to  his  son  and  | 
to  his  daughter.  What  part  of  his  property  did  he  will  to 
both? 

5.  From  my  house  to  my  grandmother's  is  |^  of  a  mile ; 
from  there  to  my  uncle's  is  |  of  a  mile.  How  far  from  my 
house  to  my  uncle's? 

6.  A  traveler  went  ^  of  his  journey  on  Monday,  ^^  on 
Tuesday,  -^  on  Wednesday,  and  1  on  Thursday.  What  part 
of  his  journey  did  he  go  in  the  four  days? 

7.  A  tailor  used  |  of  a  piece  of  cloth  in  making  one  suit, 
and  ^  of  the  piece  in  another  suit.  What  part  of  the  piece 
did  he  use  in  the  two  ? 

8.  A  milkman  leaves  J  of  a  gallon  of  milk  at  one  house, 
|-  of  a  gallon  at  another,  and  J  of  a  gallon  at  anotlier.  How 
much  does  he  leave  at  the  three  houses  ? 

9.  Anna  put  ^  of  a  dollar  in  the  bank,  she  paid  f  of  a 
dollar  for  ribbon,  and  J^  of  a  dollar  for  car  fare.  What  part 
of  a  dollar  did  she  spend  altogether  ? 

10.  A  gardener  planted  ^  of  his  garden  in  sweet  peas,  |  in 
carnations,  and  -^-^  in  violets.  What  part  of  his  garden  is 
planted  in  peas,  carnations,  and  violets? 

11.  John  used  |^  of  a  pound  of  nails  in  building  a  boat,  and 
^  of  a  pound  in  building  a  coaster.  What  part  of  a  pound 
did  he  use  ? 

12.  A  tailor  uses  |-  of  a  yard  of  cloth  in  making  the  jacket, 
and  ^J  of  a  yard  in  making  the  trousers,  of  a  boy's  suit.  How 
many  yards  in  the  suit  ? 

13.  Amy  practices  her  music  lesson  for  ^  of  an  hour 
and  sews  for  -f^  of  an  hour.  How  long  does  she  sew  and 
practice  ? 


FRACTIONS  103 

14.  Harry  and  James  started  from  a  certain  point  and 
walked  in  opposite  directions.  When  Harry  had  walked  f 
of  a  mile  and  James  ^J  of  a  mile,  how  far  apart  were  they  ? 

15.  Laura  has  done  f  of  a  yard  of  hemming  and  her  sister 
J  of  a  yard.     How  much  have  the  two  girls  done  ? 

16.  What  is  the  sum  of  |-  yd.  and  |  yd.  ? 

17.  -^y  rod  and  ^  rod  are  how  many  rods  ? 

18.  Y^  acre  and  ^^  acre  are  how  many  acres  ? 

19.  Add  f  lb.,  f  lb.,  i  lb.,  and  f  lb. 

20.  Add  ^^  da.  and  |  da. 

152 

1.   I-I 

i-i 
I-* 
i-i 
i-i 
I-I 

5_4 
6        6 


f- 


A 


4 
9 


5-  i-i 
i-S 
i-i 

f-i 

^2-i 


A- 1 

3 

•  Hi- 

-1 

4. 

■  I-I 

il-f 

i+k- 

-\ 

I-tV 

M-l 

*+i- 

-J 

f-l 

I-I 

l+i- 

4 

i-l 

f-A 

l+f- 

-i- 

I-i 

f-i 

l+i- 

-tV 

f-l 

ff-l 

A-f- 

-A 

4-tV 

i!-^ 

A-i- 

-i 

f-i 

I-I 

ii-l- 

-i 

A-i 

L^-l 

il-f- 

4 

f-f 

6.    ^#- 

-i 

7 

•    il- 

■I-I 

.           ¥- 

-1 

M- 

■f-l 

¥- 

-1 

T^- 

'A— 1% 

f*- 

-t 

li- 

■A-f 

¥- 

-i 

M- 

■-i-f 

4^- 

-1 

M- 

■I-t's 

¥- 

-i 

M- 

■I-I 

104 


AlilTHMETIC   WITHOUT   A  PENCIL 


153 

1.  Gerald  had  |  of  a  dollar  and  spent  |  dollar.  How  much 
did  he  save  ? 

2i  A  man  owned  ij  of  an  acre  of  land  and  sold  |  of  an 
acre.     What  part  of  an  acre  remained  unsold  ? 

3.  Amy  had  |  of  a  yard  of  hemming  to  do.  When  she  had 
hemmed  ^^  of  a  yard,  what  part  of  a  yard  had  she  still  to  hem  ? 

4.  A  gardener  owns  ^  of  an  acre  of  land;  |  of  an  acre  is 
planted  in  roses  and  the  rest  of  his  land  in  violets.  What 
part  of  an  acre  is  in  violets  ? 

5.  A  man  owned  a  |  interest  in  a  mine.  He  sold  ^  of  the 
mine.     What  part  of  the  mine  did  he  still  own  ? 

6.  Roy  lives  1|  of  a  mile  from  school.  If  he  rides  |^  of  a 
mile  what  part  of  a  mile  has  he  to  walk  ? 

7.  John  had  |^  of  a  pound  of  nails.  He  used  f  of  a  pound  in 
building  a  pigeon  house.     What  part  of  a  pound  had  he  left  ? 

8.  James  earned  ^  of  a  dollar  and  Reginald  J  J  of  a  dollar. 
Which  earned  more,  and  .how  much  more  ? 

9.  Rollo  did  ^  of  a  piece  of  work  and  Roy  did  |.  Which 
did  more,  and  how  much? 

10.  Joe  ran  ^^  of  a  mile.  Henry  ran  f  of  a  mile.  Which 
ran  farther  and  how  much  ? 


154 

Find  sum  of  and  difference  between 
1.    %i  2.    11    li 

4.    1J,J  5.    lj,li 


3.    1J,| 
9-    IJ'I 


FRACTIONS  105 

10.  11,  i  11.  If,  IJ  12.  If,  i 

13.  IJ,  i  14.  li    li  15.  If,  I 

16.  li  i  17.  li  H  18.  1|,  I 

19.  4,  i  20.  li  11  21.  11,  f 

22.  11,  Jo  23.  H,  I3-V  24.  1  j,  3-9^ 

25.  11    1  26.  1|,  IJ  27.  If,  11 

28.  H,  i  29.  If,  IJ  30.  1|,  If 

31.  H,  J  32.  1|,  1^-  33.  IJ,  If 

34.  11,  i  35.  If,  11  36.  If,  If 

37.  1^0,  i  38.  1 J^,  11  39.  1,-V  1| 

40.  11,1V  «•  1^1^  42.  11,1^ 

155 

1.  Margaret  has  1^  yards  of  ribbon  on  her  hat  and  ^  of 
a  yard  for  her  hair.  How  many  yards  has  she  in  the  two 
pieces  ? 

2.  Willie  lives  If  miles  from  school.  Robert  lives  1^ 
miles  from  school  in  the  opposite  direction.  How  far  apart 
do  they  live  ? 

3.  John  and  his  brother  bought  a  present  for  their 
mother.  John  contributed  1|  dollars  and  his  brother  $  2J. 
What  did  the  present  cost  ?  . 

4.  Henry  chopped  1^  cords  of  wood  in  one  week  and 
2^  cords  the  next.  How  much  did  he  chop  in  the  two 
weeks  ? 

5.  Amy  gathered  If  pecks  of  berries,  while  Jane  gathered 
If  pecks.     How  much  did  the  two  girls  gather  ? 


106  ARITHMETIC   WITHOUT   A  PENCIL 

6.  A  man  owns  two  cows  ;  one  gives  2J  gallons  of  milk 
a  day  and  the  other  gives  IJ  gallons.  How  much  do  both 
give? 

7.  Robert  paid  f  1|^  for  books  and  $  1^  for  repairs  to  his 
bicycle.     What  did  he  pay  for  all  ? 

8.  Myrtle  paid  $1  for  a  car  ticket,  $1^-^  for  thread, 
needles,  and  thimble,  and  ||-  for  ribbon.  How  much  did 
she  spend  ? 

9.  In  going  a  journey  Harry  traveled  12|-  miles  by  boat 
and  10|  miles  by  cars.     How  long  was  the  journey  ? 

10.  Two  men  started  from  the  same  point  and  traveled 
in  opposite  directions,  one  at  the  rate  of  9f  miles  per  hour, 
and  the  other  at  the  rate  of  8|  miles  per  hour.  How  far 
apart  were  they  at  the  end  of  an  hour  ? 


3.  2J-1| 

6-  3|-1| 

12.  10^1-9^ 

15.  1214 -lOf 

18.  15f-10J 

!>1  911—11 


1. 

2-1 

4. 

8-} 

7. 

3-1 

10. 

4-i 

13. 

2-f 

16. 

8-1 

19. 

1-1% 

22. 

12-1 

25. 

10-f 

28. 

20-A 

31. 

24- A 

34. 

25-t 

37. 

25-A 

40. 

39-A 

156 

2. 

2-l| 

5. 

5-li 

8. 

7-li 

11. 

12 -If 

14. 

12 -2| 

17. 

21 -5| 

20. 

20 -2f 

23. 

25-10-1 

26. 

30-91 

29. 

36 -8| 

32. 

40  -  201 

35. 

44  -  25  J 

38. 

45-161 

41. 

50 -IJ 

24.  17J-15J 

27.  50f-25i 

30.  27J-20 

33.  3511-30 

36.  28f-4J 

39.  49f-J^. 

42.  63f-J 


FRACTIONS  107 

167 

1.  From  a  piece  of  beef  weighing  40  pounds,  lOJ  pounds 
were  cut.     How  much  did  the  remainder  weigh  ? 

2.  A  grocer  had  100  pounds  of  dates.  He  sold  35|  pounds. 
How  many  pounds  had  he  left  ? 

3.  I  had  a  journey  of  36^  miles  to  go.  After  I  had 
traveled  25  miles  how  much  had  I  still  to  travel  ? 

4.  Roy  traveled  24|  miles  by  cars  and  20J  miles  by  boat. 
How  much  farther  did  he  travel  by  cars  than  by  boat  ? 

5.  A  farmer  has  15^^^  acres  of  corn  and  12|^  acres  of 
wheat.     How  many  more  acres  of  corn  than  wheat  has  he  ? 

6.  In  one  tent  there  are  48|  yards ;  in  another  there  are 
40^3^  yards.     How  much  more  in  the  first  than  in  the  second  ? 

7.  Laura  has  $  25^^^  in  the  bank.  How  much  more  must 
she  put  in  so  as  to  have  $  50  ? 

8.  June  spent  127^  and  Laura  spent  #21^.  How  much 
more  did  June  spend  than  Laura  ? 

9.  It  is  20|  miles  from  my  home  to  my  cousin's  and  15| 
miles  to  my  uncle's.  How  much  farther  to  my  cousin's  than 
to  my  uncle's  ? 

10.   A  girl  used  5J,  yards  from  a  piece  of  lace  containing 
25  yards.     How  many  yards  had  she  still  in  the  piece  ? 


158 

1-  H-i    ■ 

2.  4i-lJ 

3.  7f-4| 

*•  H-i 

5-  ^-^ 

6.  25J-17f 

'•  H-i 

8.  H-n 

9.  80f-20f 

10.  ^-i 

11.  ^-^ 

12.  12T»^-10i^ 

108  ARITHMETIC   WITHOUT   A   PENCIL 


13. 

3|-| 

14. 

3|-H 

15. 

24tV 

-151 

16. 

H-l- 

17. 

H-H 

18. 

80f- 

■  251J 

19. 

10|-f 

20. 

lof-if 

21. 

45J- 

-16,1 

22. 

20J-i'ff 

23. 

20J-1A 

24. 

30J- 

-28J 

25. 

Wo-t'o 

26. 

15#^-1A 

27. 

50,-V 

-12^»B 

28. 

H-i 

29. 

8i-lJ 

30. 

48A 

-40| 

31. 

15i-f 

32. 

15i-lf 

33. 

26f- 

-20f 

34. 

17f-i 

35. 

12i-f 

36. 

16|- 

-lOf 

159 

1.  From  a  barrel  containing  31|-  gallons  of  vinegar,  20| 
gallons  were  drawn.     How  many  gallons  remained? 

2.  3J  yards  of  string  were  lost  from  a  kite  string  contain- 
ing SO^  yards.     How  long  was  the  string  then  ? 

3.  7J  gallons  leaked  out  of  a  cask  containing  20;^  gallons. 
How  many  gallons  were  left  ? 

4.  Arnold  saved  f  12|^  last  month  and  $15 J  this  month. 
How  much  more  did  he  save  this  month  than  last  month  ? 

5.  Bertha  made  3|-  yards  of  lace.  Her  sister  made  4J 
yards.     How  much  less  did  Bertha  make  than  her  sister  ? 

6.  It  required  5|  yards  to  make  a  skirt  and  1|^  yards  to 
make  a  waist.  How  many  more  yards  in  the  skirt  than  in 
the  waist  ? 

7.  Two  boys  started  from  the  same  point;  one  traveled 
12|  miles  per  hour  and  the  other  10|  miles  per  hour  in  the 
same  direction.  How  far  apart  were  they  at  the  end  of  an 
hour? 

8.  Frank  gave  his  sister  f  1|^.  He  gave  his  brother  $2^. 
How  much  more  did  he  give  his  brother  than  his  sister  ? 


FRACTIONS  109 

9.    I  paid  $65^  for  a  horge  and  sold  liim  for  f  87J.     How 
much  did  I  gain  ? 

10.  If  a  ton  of  hay  cost  $10 J  and  was  sold  for  |11|,  how 
much  was  gained  ? 

11.  A  man  raised  150  bushels  of  potatoes.  He  sold  all 
but  30J  bu.     How  much  did  he  sell  ? 

12.  A  farmer  owned  12^^  acres  of  land  and  bought  10 J 
acres  more.     How  much  had  he  then  ? 

13.  After  29J  rods  of  fence  had  been  built,  15J  yards 
remained  to  be  built.     How  long  was  the  fence  to  be  ? 

14.  I  had  $40  in  the  bank.  I  put  in  1 25|  more  and  after- 
ward drew  out  $  20|.     How  much  then  remained  ? 

15.  There  are  30  acres  in  my  farm.  3J  acres  are  in  orchard, 
5|  acres  are  in  grain,  and  the  remainder  is  pasture  land.  How 
many  acres  of  pasture  have  I  ? 

16.  From  a  bin  containing  30|  bu.  of  oats,  2J  bu.  were 
sold  at  one  time  and  10  bu.  at  another  time.  How  many 
bushels  were  left  in  the  bin  ? 

17.  Jesse  earned  $5|-  last  week  and  |3|  this  week.  He 
put  all  but  $5  in  the  bank.  How  much  did  he  put  in  the 
bank? 

18.  After  selling  5|  dozen  eggs,  a  boy  had  Tf  dozen  left. 
How  many  had  he  at  first  ? 

19.  Mason  read  55J  pages  yesterday,  and  10  pages  to-day. 
There  are  100  pages  in  the  book.  How  many  pages  has  he 
yet  to  read  ? 

20.  One  room  required  32^  yards  of  carpet ;  another,  29| 
yards.     How  many  yards  in  both  rooms  ? 


110 


ARITHMETIC 

WITHOUT 

A 

PENCIL 

160 

i+i=l=l 

Ki  = 

2xi=f=| 

2xi  = 

Jx  2  =  1  =  1- 

1x2  = 

2 
3 

1.  A  boy  paid  $  J  for  each  one  of  2  balls.     What  did  he 
pay  for  both  ? 

2.  He  bought  2  books  at  a  quarter  apiece.     What  did  they 
cost? 

3.  Milton  had  1 2.     He  gave  away  one-fourth  of  it.     How 
much  did  he  give  away  ? 

4.  How  much  will  2  bottles,  containing  J  ounce  each, 
hold? 

5.  A  man  had  2  acres  of  land  and  sold  ^  of  it.    How  many 
acres  did  he  sell  ? 


'■-H= 

1 

'2 

2 

2 

8.    3x|  = 

'•-H= 

=  2 

2     1 

1       2 

lof^=2 

^•^4= 

I.x5  = 

10 


10.  I  of  12  =  ?    11.   8xf=?    12.   9xf=?    13.   16xf=? 
12xf=?  fx8=?  |x9=?  fxl6=? 


FRACTIONS  111 

161 

1.  There  are  3  feet  in  a  yard.     How  many  feet  in  ^  yard  ? 

2.  How  many  feet  in  |^  yd.  ?     In  -f^  yd.  ? 

3.  There  are  4  qt.  in  a  gallon.     How  many  quarts  in 
I  gal.?    IiiTJjgaL? 

4.  What  will  6  tops  cost  at  $|^  each  ?  • 

5.  8  pieces  of  ribbon  f  of  a  yard  long  contain  how  many 
yards  ? 

6.  I  bought  5  pounds  of  candy  at  -f-^  of  a  dollar  per 
pound.     What  did  it  cost  ? 

7.  When  calico  is  10  cents  a  yard,  what  does  f  of  a  yard 
cost  ? 

8.  There  are  8  pints  in  a  gallon.     How  many  pints  in 
•f^  gallons  ? 

9.  At  75  cents  a  pound,  what  will  -^^  of  a  pound  of  tea 
cost  ? 

10.    At  $2  a  ton,  what  will  |  ton  hay  cost  ? 

162 

1.  f  of  36     ^1  of  m       \l  of  132  I  of  64  f  of  54 

2.  if  of  110    f  of  56        f  of  48  ^2  of  120  f  of  63 

3.  3   of  42      ^  of  144      I  of  63  f  of  40  f  of  120 


4. 

15x| 

72x| 

36xf 

8X3>j 

S. 

63x| 

72xf 

36  xf 

9xjV 

6. 

84  xf 

72  xf 

36xii 

8xi^ 

7. 

96xf 

72x,% 

36xf 

10x,V 

8. 

55  xf 

72  xJ^ 

36  x^ 

ISXaV 

112  ARITHMETIC   WITHOUT   A  PENCIL 

9.   ^  of  8       10.   Jj  of  22       11.    2^  of  7       12.  ^  of  2 


^^oi5 

Jjof  11 

5Vofl2 

A  of  5 

^^of3 

^'jofe 

2V  of  12 

2V  of  4 

tV  of  6 

J  of  24 

I'j  of  16 

iVof6 

^of7 

^of5 

^h  of  25 

A  of  11 

163 


1.   J  of  2  dollars  =  1  dollar. 


lof  2  thirds=l  third. 


1 

? 
2      3      3  ?     3     3 


1.21  121  1?1 


2.   J  of  6  apples  =  2  apples, 
i  of  6  sevenths  =  2  sevenths. 

2 

3       7     21     7  ^77 


1      §_  3  _1         1     ^_1 
3''7"21"7'  °'8''7~7 


^3      5_15_1         g     ?_1 
6^6~30~2'  °''^^^~2 


5. 

Axi% 

6. 

2 

7. 

f  xif 

8. 

Axf 

9. 

Axif 

10. 

fxi^^ 

11. 

Hx,V 

12. 

f   Xt^O 

13. 

|xf 

14. 

fxA 

15. 

iixi! 

16. 

|xH 

17. 

f  x| 

18. 

Axff 

19. 

1^1  x-V/ 

20. 

JxH 

FRACTIONS  118 

164 

1.  What  will  I  of  a  foot  of  moulding  cost  at  ^^  of  a  dollar 
a  foot  ? 

2.  What  will  -^^  of  a  yard  of  lace  cost  at  ^^  dollar  per 
yard  ? 

3.  What  will  |-  of  a  yard  of  carpet  cost  at  $l|  per  yard? 

4.  A  man  owned  a  -^  interest  in  a  ship  and  sold  -|  of  his 
share.     What  part  of  the  ship  did  he  sell  ? 

5.  Jessie  had  ^^2  c>f  a  pound  of  candy  and  gave  away  |  of 
it.     What  part  of  a  pound  did  she  give  away  ? 

6.  Nat  has  |  of  an  acre  in  his  garden.  He  planted  |  of 
it  in  potatoes.     What  part  of  an  acre  of  potatoes  has  he  ? 

7.  A  man  bought  a  farm  for  J^  of  its  real  value  and  sold 
it  for  ||-  of  what  he  paid  for  it.  What  part  of  the  real  value 
of  the  farm  did  he  sell  it  for  ? 

8.  Tom  has  to  weed  ^  of  the  garden.  When  he  has  done 
^  of  his  work,  what  part  of  the  garden  has  he  weeded  ? 

9.  Jack  cut  -^j  of  a  cord  of  wood  to-day  and  corded  up  ^ 
of  what  he  cut.     What  part  of  a  cord  did  he  pile  up  ? 

10.    Scott  has  \  as  much  money  as  Jack.     Jack  has  |  as 
much  as  Tom.     Scott's  money  is  what  part  of  Tom's  ? 

165 

1.    Ixf  2.    fxf  3.     ^-^jXf  4.    ^Xf 

fxf  |xf  JX|  ^^Xf 

fxi  |xf-  I  xf  |x| 

5.  Tim  had  |  of  a  pound  of  nails.  He  used  |  of  them. 
What  part  of  .a  pound  did  he  use  ? 


114  ARITHMETIC   WITHOUT   A   PENCIL 

6.  What  will  1^  of  a  pound  of  coffee  cost  at  |^  of  a  dollar 
a  pound  ? 

7.  My  ruler  was  J  of  a  yard  long.     I  cut  off  J  of  it. 
What  part  of  a  yard  did  I  cut  off  ? 

8.  I  bought  4  of  a  bushel  of  fruit.     ^  of  it  was  apples. 
What  part  of  a  bushel  of  apples  did  I  buy  ? 

9.  It  is  ^J  of  a  mile  to  school.     If  1  run  J  of  the  way, 
what  part  of  a  mile  do  I  run  ? 

10.    What  will  f  of  a  yard  of  silk  cost  at  |-  dollar  per  yard  ? 


166 

1. 

Ijx4 

2. 

5x11 

3. 

Ifx6 

4. 

Ijx6 

5. 

10x11 

6. 

lfxl2 

7. 

11x10 

8. 

12xlJ 

9. 

If  x24 

10. 

4x8 

11. 

9x11 

12. 

25  xH 

13. 

l3:Vx50 

14. 

1^^0X50 

15. 

l^j  X  22 

16. 

1^0  X 100 

17. 

50xliV 

18. 

lfx20 

19. 

ljx28 

20. 

75x11 

21. 

l|xl6 

22. 

lix40 

23. 

50x11 

24. 

l|x27 

25. 

25x11 

26. 

^1x10 

27. 

10x2f 

28. 

75xlf 

29. 

2Jxl5 

30. 

20  X  2| 

31. 

40xlf 

32. 

21x21 

33. 

13x2^3 

34. 

49xlf 

35. 

21x20 

36. 

25x22 

37. 

56xlf 

38. 

31x12 

39. 

24x21 

40. 

ISxlOf 

167 

1.  What  will  1 J  yards  of  wire  cost  at  9  cents,  a  yard  ? 

2.  What  will  20  buttons  cost  at  3^  cents  apiece  ? 

3.  What  will  25  yards  of  carpet  cost  at  f  2|  ? 

4.  How  many  are  3|  dozen  ? 


FRACTIONS  115 

5.  What  is  the  cost  of  3|  yards  of  velvet  at  $  5  ? 

6.  How  many  inches  in  1^  yards  ? 

7.  Fay  is  16  years  old.     Her  father  is  2|  times  as  old  as 
she.     How  old  is  her  father  ? 

8.  It  is  2^  miles  to  my  uncle's.     How  far  do  I  travel  in 
going  there  and  back  20  times  ? 

9.  Jack  walks  4|  miles  an  hour.     How  far  does  he  walk 
in  15  hours  ? 

10.    A  man  has  l^j  acres  of  land  planted  with  55  trees  to 
the  acre.     How  many  trees  has  he  ? 


168 

11x5 

2.   11x7 

3.    11x10 

4.  1^x15 

21x5 

2ix7 

2JxlO 

21  xl5 

31x5 

31  xT 

3^x10 

3Jxl5 

4Jx5 

4Jx7 

41  xlO 

41x15 

51x5 

51x7 

51x10 

5^x15 

5.  What  will  5  J  pounds  of  sugar  cost  at  5  cents  ? 

6.  What  will  5J  yards  of  ribbon  cost  at  10  cents  ? 

7.  What  will  15  pounds  of  berries  at  3 J  cents  cost  ? 

8.  What  will  21  lbs.  of  coffee  at  4-J-  cents  cost  ? 

9.  1^  pounds  dried  peaches  at  22  cents  cost  how  much  ? 

10.  5  quarts  of  milk  at  8|  cents  cost  how  much  ? 

11.  8f  X  3  12.  4f  X  3  13.  2-^  X  4 
14.  5J  X  9  15.  41  X  3  16.  51  X  15 
17.  5  X  7f                     18.   7J  X  4                     19.   6  X  2| 


116  ARITHMETIC   WITHOUT   A   PENCIL 


20. 

6x2^ 

21. 

5f  x6 

22. 

7x3^ 

23. 

10x2^ 

24. 

5x9^ 

25. 

3x8| 

26. 

6x2^j 

27. 

4x2| 

28. 

7x2A 

29. 

5|x3 

30. 

4^^x4 

31. 

h\  X  6 

32. 

Hi  X  7 

33. 

4Ax5 

34. 

3A  X  25 

35.  What  will  15  yards  of  tape  cost  at  6J  cents  ? 

36.  What  will  121  yards  of  velvet  at  $  8  cost  ? 

37.  2^  pounds  of  sugar  at  5  cents  cost  how  much? 

38.  Shirley  walks  3^^^  miles  an  hour.  How  far  will  he 
walk  in  7  hours  ? 

39.  Mary  makes  a  yard  of  lace  in  9|  hours.  How  long 
will  it  take  her  to  make  3  yards  ? 

40.  George  had  2^^  pounds  of  putty.  He  used  last 
month  3  times  as  much  as  he  has  now.  How  much  did 
he  use  last  month? 

41.  I  have  2^%  rows  of  apple  trees  with  8  trees  in  a  row. 
How  many  trees  have  I  ? 

42.  A  farmer  has  IO^^q-  tons  of  hay  worth  $20  per  ton. 
What  is  his  hay  worth  ? 

43.  At  •$  4ySg  a  head  what  will  4  sheep  cost  ? 

44.  At  5  cents  a  pound  what  will  2^^^  pounds  of  candy 
cost? 

169 


ixf  =  | 

2-    fxf 

3.    fxf 

4-    fxf 

ixf 

fxf 

fxf 

fxA 

ixf 

■      fxf 

fxf 

\y-\i 

FRACTIONS  lir 


5.  lixU=^x^=2 

6.  21x4  7.    2ixlJ  8.   SJxlf 
9.   11  X  21                    10.   2|  X  2f                    11.  6f  x  IJ 

12.    11  X  If  13.    1|  X  21  14.    8|  X  11 

15.   Iix2f  16.   2fxl|  17.  Iix5| 

18.   2ix2|  19.   11x21  20.  9Jx3J 

21.  How  many  quarts  of  oil  will  it  take  to  fill  1|  times  a 
jug  holding  8|-  quarts  ? 

22.  What  will  2|  yards  of  silk  at  $  2|-  per  yard  cost  ? 

23.  I  bought  lace  curtains  5J  feet  long  at  f  IJ  per  foot. 
What  did  they  cost  apiece  ? 

24.  Sara  can  hem  1^  yards  an  hour.     How  many  yards 
can  she  hem  in  1|  hours  ? 

25.  Jack  bought  for  his  rabbits  3 J  tons  of  hay  at  f  9J  a 
ton.     What  did  it  cost  ? 

26.  What  will  2|  gallons  of  ice  cream  cost  at  $  1|  ? 

27.  It  took  2J  feet  of  moulding  at  lOJ  cents  a  foot  to  make 
a  frame.     What  did  it  cost  ? 

28.  Tom  hoes  4|  rows  of  corn  in  an  hour.     How  many 
rows  can  he  hoe  in  1|  hours  ? 

29.  At  1 1 J  per  yard  what  will  IJ  yards  of  cashmere  cost  ? 

30.  At  5 J  cents  a  pint  what  will  3 J  pints  of  berries  cost  ? 

170 

1.   2  dollars  divided  between  2  girls  allows  how  much  to 
each? 

$2-»-2  =  |l.  4  acres  -j-  2  =  2  acres. 


118  ARITHMETIC   WITHOUT   A  PENCIL 

2.  6  apples  ^2  =  3  apples.     10  thirds  -^  2  =  5  thirds. 

3.  i|-v2  =  T^     f-^2  =  f 

4.  1^2  5.   ^^^8  6.   if^6 
7.  j|^2                                 8.    J^^3  9.    i|H-6 

10.  i|^2  n.  i^^T  12.  i|^3 

13.    1|^5  14.    11  + 7  15.    IJ  +  3 

16.  A  father  divided  ij  of  an  acre  equally  among  his  3 
boys  for  their  gardens.  What  part  of  an  acre  did  he  allow 
to  each  ? 

17.  Mat  divided  $|  equally  among  3  small  boys.  What 
part  of  a  dollar  did  each  receive  ? 

18.  Mary  divided  l|  of  a  pound  of  candy  equally  among 
4  girls.     What  part  of  a  pound  did  each  receive  ? 

19.  I  cut  11^  of  a  yard  of  cloth  into  8  equal  pieces.  How 
long  was  each  piece  ? 

20.  I  filled  a  bottle  3  times  from  ^  of  an  ounce  of  per- 
fumery.    How  much  did  the  bottle  hold? 

171 

1.  l|^2  =  ^^,orlf.      l|=iV      f-^3  =  for,^^.      ^  =  f 

2.  Multiplying  the  denominator  by  the  integer  will  give 
the  same  result  as  dividing  the  numerator  by  the  integer. 
Dividing  the  numerator  is  shorter  if  it  can  be  done.  When 
this  cannot  be  done,  multiply  the  denominator. 


1-^5 

4.    ^,  +  6 

5.     ^  +  3 

6.     1+11 

1-5 

^+2 

^-7 

T^-12 

1+8 

^+3 

A-6 

A-7 

^+3 

t\-6 

f+5 

^-+2 

t-^7 

1-3 

f-2 

T^-6 

r6 

-5 

J^e. 

-3 

3^0., 

^10 

3^U 

r7 

FRACTIONS  119 

7.   5;jO_^6  8.    ^H-2  9.   i^^5  10.    l^-s-S 

^H-3  ^4^7  f^^6 

¥-4  M^2  11-^7 

^H-6  11^3  11^8 

¥^9  11^4  1-1^12 

11.  I  divided  f  ||  equally  among  4  boys.  How  much 
did  I  give  each? 

12.  II  of  a  yard  of  tape  was  cut  into  5  equal  pieces.  How 
long  was  each  piece  ? 

13.  A  father  divided  ||  of  his  property  equally  among  his 
3  children.     What  part  did  he  give  each  ? 

14.  Edward  had  |  of  a  pound  of  cherries.  He  divided 
them  equally  among  3  children.  What  part  of  a  pound  did 
each  receive  ? 

15.  Norman  divided  |  of  his  garden  into  5  equal  beds. 
What  part  of  his  garden  is  each  bed  ? 

172 

1.  If  you  have  $4  divided  into  half  dollars,  how  many 
coins  have  you  ?     8  is  right. 

Then4-^l  =  8.     Now,  4x2  =  8. 

2.  If  you  have  $4  divided  into  quarters,  how  many  coins 
do  you  have  ?     16  is  right. 

Then  4-1  =  16.     Now,  4x4  =  16. 
Therefore,  4-^1  =  4  xf  =  8.         4-^1=4x^=16. 
Hence,    to   divide   by   a  fraction,  invert   the  divisor  and 
multiply.      [Look  in  your  dictionary  for  invert.'] 

3.  If  I  give  away  1 5  in  one-dollar  pieces,  I  can  give  to  5 
persons,  but  if  I  give  only  half  as  much  to  each  person,  I  can 
give  to  twice  as  many  persons;  therefore,  dividing  by  one- 
half  is  really  multiplying  by  two. 


120  ARITHMETIC   WITHOUT   A   PENCIL 

4.  $  5  given  in  dollar  pieces  can  be  given  to  5  persons ; 
given  in  quarters  it  can  be  given  to  20  persons  ;  therefore, 
if  5-^l  =  5,  then  5-^^  =  20,  and  5  x-f  =  -^-=20. 

5.  $^  given  in  quarters  can  be  given  to  how  many  persons  ? 

2-4-^^l-l-^- 

6.  What  is  true  in  these  cases  is  true  in  all  others,  there- 
fore :  To  divide  by  a  fraction,  invert  that  fraction  and  proceed 
as  in  multiplication  of  fractions. 


'■  §-= 

5 
12 

This  is 

the  same  principle, 

r               10          o 

for:    ^^-.2 

10     2 
is  — -^-,  whicl] 

lis 

5 
12' 

(Always  do 

the  shortest 

correct  method 

•) 

It 

(Look  for  the 

easiest  way.) 

8.   1^2 

9.    if  ^7 

10.  ^^5 

11.    10-1 

l^f 

iS-J 

1^2 

25^f 

I^J 

if -^2 

i-i 

12^1 

1^1 

■  f^i 

*     l-f 

12^1 

if -^5 

f^3 

i-A 

20^t 

12.  IJ  of  his  entire  crop  a  farmer  sold  in  3  equal  amounts. 
What  part  of  his  crop  was  each  sale  ? 

13.  Change  f  of  an  inch  to  the  fraction  of  a  foot. 

14.  Mae  made   |  of  a  yard  of  ribbon  into  6  badges  of 
equal  length.     How  long  was  each  ? 

15.  Rose  made  ^  of  a  yard  of  ribbon  into  badges  ^^  ^f  a 
yard  long.     How  many  badges  did  she  make  ? 

16.  If  it  takes  ^ J  of  a  yard  of  braid  to  bind  a  square  mat. 
How  long  is  one  side  of  the  mat  ? 


173 

1. 

H^i 

2J^J 

2|-^| 

5J-f 

H^i 

^H 

If^l 

^^l 

2. 

li-vlO 

H^i 

2f^5 

lA-i 

H^A 

^^i 

StV^4 

2Hi 

3. 

H^n 

H-^i 

H^i 

7j^j 

i*+i 

5i^t 

i|^} 

T^^2% 

4. 

H-^H 

2Hf 

n^i 

ii^^% 

if^i^ 

3f+l 

H^i 

if-A 

121 


5.  How  many  times  can  I  fill  a  bottle  holding  ^  of  a  pint 
from  5  J  pints  ? 

6.  How  many  times  can  I  fill  a  jug  holding  1  quart  from 
7|-  gallons  ? 

7.  If  Susie  makes  2  yards  of  lace  in  10  hours,  how  long 
will  it  take  her  to  make  1  yard  ? 

8.  If  Carrie  makes  1 J  yards  of  lace  in  9J  hours,  how  long 
will  it  take  her  to  make  1  yard  ? 

9.  If  Carrie  makes  IJ  yards  of  lace  in  9J  hours,  how 
much  will  she  m.ake  in  1  hour  ? 

10.  If  Susie  makes  2  yards  of  lace  in  10  hours,  how  much 
will  she  make  in  1  hour  ? 

11.  John  can  chop  2|  cords  of  wood  in  3 J  days.     How 
long  will  it  take  him  to  chop  1  cord  ? 

12.  How  much  can  he  chop  in  1  day  ? 

13.  4|-  yards  of  cloth  cost  1 5|.     What  did  1  yard  cost  ? 

14.  How  much  can  be  bought  for  1 1  ? 


122  ARITHMETIC   WITHOUT   A  PENCIL 

15.  3J  acres  of  land  yield  20J  tons  of  hay.     What  does  1 
acre  yield  ? 

16.  What  part  of  an  acre  yields  1  ton  ? 

17.  It  takes  4^  days  to  build  5^  rods  of  stone  wall.     How 
long  does  it  take  to  build  1  rod  ? 

18.  How  many  rods  are  built  in  1  day  ? 

19.  At  $  1|  apiece,  how  many  felt  hats  cost  $  15|  ? 

20.  If  a  man  uses  IJ  pounds  of  flour  a  day,  how  long  will 
50  pounds  last  him  ? 

21.  A  fruit  man  puts  J  of  a  pound  of  berries  in  a  box. 
How  many  boxes  will  12|^  pounds  fill  ? 

22.  When  3|-  dozen  eggs  cost  f  dollar,  what  :^  the  cost 
per  dozen? 

23.  How  many  dozen  cost  $  1  ? 

24.  If  one  book  costs  $  f ,  how  many  of  them  will  cost  $  5^  ? 

174 

1.  If  you  have  $  2  and  give  away  $  1,  what  part  of  your 
money  do  you  give' away  ?     Then  1  is  what  part  of  2  ? 

2.  1  is  what  part  of  3  ?     Of  4?     Of  5?     10? 
20?     25?     50?     100? 

3.  2  is  what  part  of  3  ?     Of  4  ?     Of  5  ?     7  ? 
30?     45?     50?     100? 

4.  3  is  what  part  of  4  ?     Of  5  ?     Of  6  ?     9  ? 
25?     75?     80?     100? 

5.  5  is  what  part  of  10  ?     Of  11  ?     Of  15  ? 
30?     70?     75?     100? 

6.  10  is  what  part  of  30?     40?     45?     50? 
100?    150?     200? 


12? 

15? 

18? 

20? 

15? 

24? 

20? 

25? 

60? 

75? 

FRACTIONS  123 

7.  A  man  had  45  sheep  and  sold  10.     What  part  of  his 
sheep  did  he  sell  ? 

8.  In  a  farm  of  30  acres  25  acres  are  in  fruit  trees.    What 
part  of  the  farm  is  in  fruit  ? 

9.  Out  of  50  eggs  5  were  bad.     What  part  was  bad  ? 

10.  Max  had  on  his  kite  a  tail  20  feet  long.  What  part 
of  it  did  he  lose  when  3  feet  of  it  broke  off  ? 

11.  A  certain  flag-pole  is  60  feet  high.  The  flag  is  lowered 
9  feet  from  the  top.     What  part  of  the  pole  is  above  the  flag  ? 

12.  A  tree  was  36  feet  tall.  Lightning  struck  it  and 
broke  off  8  feet.     What  part  was  broken  off  ? 

13.  Carl  had  1 5  and  spent  $  21.  What  part  of  his  money 
did  he  spend  ? 

14.  A  dressmaker  has  11  yards  of  lace  for  trimming  a 
waist.  When  she  has  used  5 J  yards,  what  part  of  it  has  she 
used? 

15.  A  boy  bought  a  bicycle  for  $  45.  When  he  had  paid 
$  25,  what  part  had  he  paid  ? 

16.  10  inches  are  what  part  of  a  foot  ? 

17.  9  ounces  are  what  part  of  a  pound  ? 

18.  60  days  are  what  part  of  2  years  ? 

19.  9  months  are  what  part  of  a  year  ? 

20.  10  months  are  what  part  of  2  years  ? 

21.  16  hours  are  what  part  of  2  days  ? 

22.  27  inches  are  what  part  of  a  yard  ? 

23.  75  cents  is  what  part  of  f  1.50  ? 

24.  9  eggs  are  what  part  of  5  dozen  eggs  ? 

25.  10  cents  is  what  part  of  1 2  ?     $  20  ? 


124  ARITHMETIC    WITHOUT   A   PENCIL 

26.  55  minutes  are  what  part  of  an  hour  ? 

27.  72  years  are  what  part  of  a  century  ? 

28.  18  is  what  part  of  a  score  ? 

29.  3  dozen  are  what  part  of  4  score  ? 

30.  4  score  and  10  years  are  what  part  of  a  century  ? 

31.  $  1.25  is  what  part  of  1 2.50  ? 

32.  1 1. 25  is  what  part  of  f  5. 00  ? 

33.  $  12.50  is  what  part  of  1 25.00  ? 

34.  1 1.50  is  what  part  of  $  4.50  ? 

35.  I  7.50  is  what  part  of  1 15  ? 

36.  1 .25  is  what  part  of  $  25.00  ? 

37.  $  2.50  is  what  part  of  1 25.00  ? 

38.  1 25  is  what  part  of  $  200  ?  , 

39.  \  is  what  part  of  -|  ? 

40.  ^  is  what  part  of  J  ? 

41.  12 J  is  what  part  of  100  ? 

42.  37|-  is  what  part  of  100  ? 

43.  12|  is  what  part  of  371  ? 

44.  37lis  what  part  of  621? 

45.  121  is  what  part  of  621  ? 

Re-write  this  exercise  as  examples  in  division. 

46.  121  is  what  part  of  25  ?     Of  50? 

47.  What  part  of  10  is  31  ?     6f  ?  ' 

48.  5 J  is  what  part  of  16|  ? 

49.  1  is  what  part  of  10  ?     Of  1000? 

50.  1  is  what  part  of  10  ?     Of  16  ? 


FRACTIONS  125 

175 

1.    6  is  J  of  what  ?  2.  7  is  J  of  what  ? 

3.   10  is  1  of  what  ?  4.  9  is  j  of  what  ? 

5.    12  is  iV  of  what  ?  6.  7  is  -|  of  what  ? 

7.    9  is  I  of  what  ?  8.  15  is  ^  of  what  ? 

9.    12  is  1  of  what  ?  10.  20  is  -^^  of  what  ? 

11.    4  is  3-V  of  what  ?  12.  25  is  ^  of  what  ? 

13.    17  is  J  of  what  ?  14.  5|  is  |-  of  what  ? 

15.    21  is  1  of  what  ? 


176 

1.  Scott  spent  $2 J,  which  was  J  of  what  he  had.     How 
much  had  he  at  first  ? 

2.  12  square  inches  are  -f^  of  a  square  foot.     How  many 
square  inches  in  a  square  foot  ? 

3.  5^  feet  are  ^  of  a  rod.     How  many  feet  in  a  rod  ? 

4.  Bert  walked  7  miles,  which  was  -J  of  the  distance  from 
his  home  to  town.     How  far  did  he  live  from  town  ? 

5.  A  dairyman  bought  5  cows,  which  were  ^  as  many  as 
he  already  had.     How  many  had  he  at  first  ? 

6.  15  years  is  1  of  my  father's  age.     How  old  is  he  ? 

7.  21  days  are  what  part  of  the  month  of  April  ? 

8.  A  merchant  sold  cloth  so  as  to  gain  15  cents,  which 
was  I  of  the  cost.     What  was  the  cost  ? 

9.  Roy  sold  his  bicycle  at  $  10  below  cost,  thereby  losing 
•J-  of  the  cost.     What  was  the  cost  ? 

10.    20  pounds  are  ^  of  my  weight.     What  do  I  weigh  ? 


126 


ARITHMETIC   WITHOUT   A   PENCIL 


177 


1.   8  is  f  of  what  ?  8-i-f=8xf  =  12. 

If  8  is  2  thirds,  1  third  is  J  of  8,  or  4,  and  3  thirds  are 
3  X  4,  or  12. 


Analyze : 

2.    8  is  f  of  what  number  ? 
4.    10  is  1^  of  what  number? 
6.  14  is  j^  of  what  number  ? 
8.    16  is  4  of  what  number  ? 


9  is  1^  of  what  number  ? 

12  is  f  of  what  number  ? 

15  is  I"  of  what  number  ? 

18  is  -f^  of  what  number  ? 
10.  24  is  -fj  of  what  number  ?  11.  24  is  f  of  what  number  ? 
12.  24  is  I  of  what  number  ?  13.  24  is  -I  of  what  number  ? 
14.  30  is  ^^  of  what  number  ?  15.  75  is  |  of  what  number  ? 
16.    80  is  I  of  what  number?     17.    72  is  |  of  what  number  ? 

18.  144  is  J^  of  what  number  ? 

19.  132  is  ^J  of  what  number  ? 

20.  108  is  -j^Q-  of  what  number  ? 

21.  100  is  -^Q  of  what  number  ? 
State  again  as  examples  in  division. 


178 

1.  I  sold  a  cow  for  $  72,  which  was  ^^  of  what  I  paid  for 
her.     What  did  3he  cost  ? 

2.  A  furniture  dealer  gained  $6  on  the  sale  of  a  set  of 
furniture,  which  was  gy  of  the  cost.     What  was  the  cost  ? 

3.  When  Jane  is  12  years  old  she  will  be  -^j  as  old  as  her 
mother  is  now.     How  old  is  her  mother  ? 


DECIMALS 


127 


4.  12  cubic  feet  are  |  of  a  cubic  yard.     How  many  cubic 
feet  in  a  cubic  yard  ? 

5.  60  square  inches  are  ^^2  of  a  square  foot.     How  many 
square  inches  in  1  sq.  ft.  ? 

6.  I  have  96  cu.  ft.  of  wood.     This  is  |  of  a  cord.     How 
many  cubic  feet  in  1  cord  ? 

7.  If  49  rods  is  -^-^  of  the  distance  around  a  field,  how 
many  rods  of  fence  will  inclose  the  field  ? 

8.  I  have  24  yards  of  matting.     It  will  cover  |  of  my 
floor.     How  many  yards  more  must  I  bu}^  ? 

9.  f  of  45  is  -j^  of  what  ? 
10.   f  of  80  is  -jSj  of  what  ? 


DECIMALS 

179 

Read  these  decimal  fractions  : 

[Be  sure 

;  to  sound  ths  and  dthsJ] 

1.    Tenths: 

2.    Hundredths : 

.5 

.25 

.16 

.63         .04 

.52 

.38 

.8 

.50 

.19 

.66         .01 

.47 

.52 

.3 

.75 

.18 

.72         .03 

.95 

.85 

.1 

.45 

.13 

.81         .08 

.34 

.09 

3.    Thousandths : 

125          .963 

.205 

.025 

.005 

.040 

.112 

258          .289 

.401 

.067 

.007 

.004 

.375 

315          .417 

.803 

.018 

.002 

.104 

.012 

429          .211 

.605 

.042 

.004 

.400 

.009 

4.   .75,   .009,  .5,   .05  .005,   .017,  .125,   .304,   .9,  .7,   .07, 
,007,  .485,  .085,  .805,  .850,   .419,  .08,  .8.  . 


128 


ARITHMETIC   WITHOUT   A   PENCIL 


5.  Ten-thousandths : 
.3275    .1049    .0375 
,5037    .9957    .0258 
,2348    .8304    .0401 
.3705    .1825    .0725 

6.  Hundred-thousandths : 
.27285     .07423     .00842 
.49407     .01247     .00705 
,12025     .02734     .00203 
,58003     .01375     .00420 

7.  .037,  .0025,  .19,  .009,  .18275,  .028,  .80307,  .4901,  .4, 
,004,  .00015,  .75075,  .0075,  .00075. 


0045 

.0103 

.0008 

0027 

.0560 

.0005 

0018 

.0702 

.0101 

,0075 

.0003 

.0004 

.01007 

.10058 

.04703 

.10005 

.02005 

.70302 

.08009 

.08704 

180 

1.  How  many  decimal  places  are  required  for  tenths  ? 
For  hundredths  ?  For  thousandths  ?  For  ten-thousandths  ? 
For  hundred-thousandths  ? 

2.  What  is  the  third  place  to  the  right  of  the  decimal 
point  called  ?  The  fourth  ?  The  first  ?  The  second  ?  The 
fifth? 

Read  these  decimal  fractions,  or  decimals : 

3.  Millionths  : 

.000005  .007125  .290204  .000875 
.000025  .027125  .075008  .087500 
.000125       .427125       .840005       .008750 

4.  .0317,  .29,  .70203,  .839,  .001275,  .02,  .00002,  .76,  .01, 
.003,  .39152,  .1752,  .017017. 


DECIMALS 

181 


129 


1.  What  is  the  name  of  the  fourth  place  ?     The  fifth  ? 
The  sixth  ? 

2.  How  many  places  are  required  to  write  millionths  ? 

3.  What  is  the  name  of  the  place  next  after  millionths  ? 

4.  How  many  places  are  required  to  write  ten-millionths  ? 

5.  Read  the  decimals  described  as  follows : 

Point,  two,  five.  Point,  nought,  seven,  five.  Point, 
eight,  nought,  five,  nine.  Point,  four,  two,  nought,  five. 
Point,  nought,  nought,  seven,  three.  Point,  eight,  nought, 
one. 

Read  these  decimal  fractions : 


6.  .5   7. 

.05  8. 

.005  9. 

.0005  10. 

.00005  11. 

.121 

.2 

.02 

.002 

.0002 

.00002 

.871 

.9 

.19 

019 

.0019 

.00019 

.081 

.7 

.28 

.028 

.0028 

.00028 

.14f 

.8 

.08 

.175 

.0175 

.00175 

.06^ 

.3 

.25 

,025 

.1275 

.01275 

.331 

.4 

.04 

.004 

.2704 

.21735 

.66f 

.1 

.003 

.0001 

.2107 

.575 

.111 

.01 

.303 

.0017 

.2115 

.6830 

.09,1 

.11 

.033 

.0175 

.371 

.511 

.55^ 

.011 

.625 

.2175 

.621 

.011 

.28f 

.511 

.875 

.2017 

.83J 

.001 

.371 

.001 

.375 

.2007 

.161 

.111 

.621 

130  ARITHMETIC   WITHOUT  A   PENCIJj 

Read  these  mixed  numbers  : 
12. 


1.12J 

13.  1.000005 

14.  9.4 

1.62J 

1.000007 

5.075 

3.331 

17.000009 

11.004 

5.871 

19.00006 

6.0025 

12.05 

21.0008 

12.1001 

25. 08  J 

11.000018 

3.1416 

75.0075 

7.000175 

8.2525 

2.661 

4.001275 

4.66| 

59.059 

9.025249 

5.371 

10.003 

1.256207 

7.0621 

182 

Addition :   [Keep  points  in  a  straight  line.] 

1.    .1  2.    .25  3.   .37 

.3  .12  .03 

.4  .27  .18 

.1  .08  .32 


7.    .7        .9        .6 

.8        .3        .7 


8.  .07      .09      .06      .05      .07      .06      .06      .09      .08      .05 
j08^.^^^.^^^^^ 

9.  .25      .37      .18      .03      .17      .75      .82      .37      .15      .65 
.05      J^      A9      ^      JL8      .^3      ^     ^      ^     ^ 

10.    .75      .85      .64      .29      .47      .18      .49      .37      .56      .65 
.25      .15      .55      .91      .97      .87      .57      .78      .56      .65 


4.  .015 

5.  .3 

6.  .18 

.003 

.2 

.25 

.104 

.1 

.37 

.375 

.1 

.14 

7 

.6   .6 

.9 

.9   .09 

7 

.8   .5 

.6 

.9   .09 

DECIMALS 

131 

11. 

.003 

.017 

.125         .358 

.063 

.955        .725 

.005 

.018 

.075         .724 

.847 

.055        .825 

12. 

.25 

.25    .025 

.025    .025    .25 

.025 

.025 

.025      .75 

•1_ 

.05    .5 

.05      .005    .25 

.025 

.25 

.0025    .75 

13. 

.75 

.75     .75 

.075     .005     1.25     1.25     3.45     146.25 

.25 

.5       .05 

.05       .075       A 

5 

.75 

.77       13.75 

14 

15 

16         17 

18           19 

20 

21 

22           23 

.5 

.8 

.05      .08 

.15      13.5 

.09 

4.4 

.14        .9 

.3 

.9 

.03      .09 

.17          .6 

.11 

.7 

.04        .3 

.7 

.1 

.07      .01 

.121        .5 

.13 

.15 

.11        .4 

.5 

.5 

.05      .05 

.13        1.3 

.03 

.5 

1.01        .7 

.6 

.6 

.06      .06 

.05        1.5 

.14 

.1 

.5          .6 

.9 

.2 

.09      .02 

.071        .41 

.5 

.7 

1.121      .8 

183 

Subtraction :   [Keep  points  in  a  straight  line.] 

1.  1.00      1.25      1.00       1.00       1.00       1.00       1.00  .75 

.05        .75        .871       .371      .66f       .Oil       .08^  .005 

2.  .875       .5      1.00         1.00         .95         .871       .66|  .63 
.5          .05       .625         .121       .095       .37i       .331  .025 


^  .^^3 


2.00       3.50      5.00        15.25        25.25       .875       150. 
1.75       1.75      2.175        8.125        9.50       .666|  .m 


4.   17.00       100.50       100.  100.  7.  10.         75.75 

.875       13.625       66.0^       66.75        .55       1.85       9.85 


132  ARITHMETIC   WITHOUT   A   PENCIL 

184 

Multiplication :  [Point  off,  from  the  right  in  the  product, 
as  many  decimal  places  as  there  are  in  both  multiplier  and 
multiplicand.] 

12  345  67  89 

.25         .9  .09        .09       .09  9       2.5         .12     1.2 

.5         .8  .8        .08         .8  .8  .5  .8       .8 


12 

12 

12 

.25 

.001 

.001 

.001 

1.00 

2.5 

.8 

.8 

.08 

.05 

5 

.5 

.05 

.05 

.05 

,125 

.125 

1.25 

12.5 

25 

.125 

1.25 

12.5 

125 

8 

.8 

.8 

.8 

.5 

.08 

.08 

.08 

.08 

2.5 

25 

75 

66 

56 

1.5 

1.5 

15 

.15 

.5 

.01 

.001 

.1 

.01 

.5 

.05 

.5 

.05 

185 

Division :  [Point  off  from  the  right  in  the  quotient,  as 
many  decimal  places  as  those  in  the  dividend  exceed  those 
in  the  divisor.     Exceed  means,  are  greater  than.~\ 


1 

l).l 

2 

1}.01 

3 

.1^ 

4 

.1).01 

5 

.1).001 

6 

.01)1.00 

.01). 10 

.01)1.10 

.01). 001 

.5)2.5 

.5)25 

.5). 25 

5)25 

5)2.5 

5).  25 

5). 025 

.05). 025 

.005). 025 

8)1.00 

12)1.00 

3)1.00 

8)64 

8).  64 

.8)64 

.8). 64 

.3)2.7 

5).16 

.02)1.3 

.07)14 

.25)100 

.i}18 

.1)1.8 

.1).18 

1)1.8 

.01)1.8 

.01)18 

DECIMALS  133 

186 

Some  reasons  why  : 

1.  Addition  :  -L  +  1-  =  -^^.     Therefore,  .1  +  .1  =  .2. 

.1 

Hence ;  JL  and  the  rule  for  pointing  off  the  sum. 

7       5       2 

2.  Subtraction  :  tt:  ~  tt;  =  :j —     Therefore,  .7  —  .2  =  .5. 

.7 
Hence;  .2  and  the  rule  for  pointing  off  the  remainder. 
T5 

3.  Multiplication  :  -^  x  :^  =  ~    Therefore,  .3  x  .4  ==  .12. 

.3 
Hence ;    x  .4  and  the  rule  for  pointing  off  the  product. 
~l2 

Memorize  rule. 

5 

4.  Division :    Jfo  -  fo  =  li^  ^  7  =  IM-        '^^^^^^°^^' 
.025  ^.5  =  .05. 

K\  Q25 

Hence  ;   *   ^ — -  and  the  rule  for  pointing  off  the  quotient. 
.05 

Memorize  rule. 

Prove  many  examples  in  division  of  decimals. 

5.  Would  you  rather  have  1 100.  or  11.00  or  f.lOO  ? 
Remember  that  the  decimal  point  is  powerful,  and  learn  to 

place  it  right. 


134  ARITHMETIC   WITHOUT   A   PENCIL 

187 

UNITED  STATES  MONEY 

10  mills  make  1  cent. 

10  cents  make  1  dime. 

10  dimes  make  1  dollar. 

10  dollars  make  1  eagle. 

20  dollars  make  1  double-eagle. 

1.  Why  is  this  a  very  easy  table  with  which  to  work  ? 

2.  What  is  such  a  system  called  ? 

This  is  an  easy  table  to  work  with  because  the  scale  is  10. 
Such  a  system  is  called  a  decimal  system,  from  a  word  in 
Latin  which  means  ten, 

3.  Why  is  a  decimal  system  easy  ? 

Because  changing  to  higher  or  lower  denominations  re- 
quires only  the  moving  of  the  decimal  point. 

4.  Multiply  each  of  these  numbers  by  10,  then  by  100, 
then  by  1000.  Describe  resulting  numbers;  as,  1,  5,  7,  0, 
point,  and  read  : 


6. 

20. 

157. 

11250. 

1   2.50 

$   5.25 

$   1.121 

7. 

25. 

239. 

1 3295. 

117.40 

$   6.75 

$     .371 

3. 

13. 

560. 

$1627. 

$11.90 

113.96 

$   5.621 

8. 

70. 

942. 

14274. 

1   8.70 

$   7.85 

$     .66| 

4. 

68. 

729. 

1 2875. 

$10.20 

$44.47 

$10,871 

Rule.  —  To  multiply  by  1  with  any  number  of  ciphers 
move  the  decimal  point  as  many  places  to  the  right  as  there 
are  ciphers  in  the  multiplier. 


DECIMALS  136 

5.  Division  is  always  the  opposite  operation  to  multiplica- 
tion. Make  the  rule  for  dividing  by  1  with  any  number  of 
ciphers. 

Divide  these  numbers  by  10, 100, 1000.  Describe  resulting 
numbers  ;  as,  point,  1,  2,  5,  and  read  : 


1.25 

27.35 

.875 

15.009 

3.0275 

7.36 

9.72 

.027 

24.1235 

.864 

11.45 

55.13 

-.5 

149.25 

17.8 

25.25 

1.75 

1.2 

14.8 

3.005 

7.50 

20.95 

.145 

27.02 

26.75 

188 

Change  these  decimal  fractious  to  common  fractions  : 


1.    .1  =  J^             2. 

•5  =  A  =  i 

•25  =  ,^  = 
.50 

=  i        3. 

.80 

4.    .24 
.55 

.3 

.75 

.90 

.65 

.7 

.45 

.70 

M 

.9 

.95 

.10 

.02 

.8 
.6 

.85 

=  2V 

.60 
.30 

.78 
.88 

.4 

.01 

.40 

.42 

.2 

.04 

.20 

.56 

[Notice  number  c 

>f  ciphers  in  denominator.] 

5.  .125=3^^  =  1 

.275 

6.  .244    7. 
.175 

.0005  = 
.0025 

10  boo  — 20  00 

8.  .0125 
.0375 

.025 

.225 

.375 

.1125 

.005 

.625 

.0075 

.0625 

.075 

.875 

.1275 

.0875 

.1375 

.475 

.0625 

.2225 

136  AKITHMETIC   WITHOUT   A   PENCIL 

189 

Change  these  common  fractions  to  decimal  fractions : 

1.  [These  are  easy  if  you  think  of  dollars  and  cents.] 

fi  -^1  I?  loi  i-Q'  TO'  TO'  2^'  20'  20'  215"'  20'  20'  2~D"'  20'  "50"'  A' 
'BTF'  "MT'  "SO"'  io'   5  0'  "^O'  F§"'  2  5'  2*5'  2P  2  5'  2^'  2^'   2  5'  2E' 

[Reduce  these  to  lowest  terms  before  changing.] 

flA      2_    _a_      4        5       18       t.     10       8        9       3 
'   2  0'   2  0'   3  0'  10'   5  0'  2  0'  TO^   2  0'  ^0'  "90'  "2  0"- 

2.  [Reduce  these  to  lower  terms ;  to  fractions  having  for 
denominators,  1  with  one  or  more  ciphers.] 

4      _1_    12     15.    10     4iL     3.1      8       12     .3.5     55. 
TO^  20'   20'  20'   50'   50'    50'  ¥0'   60'    60'   80* 

3.  You  see,  it  is  sometimes  easier  to  change  to  lowest  terms 
and  sometimes  to  lower  terms  before  changing  to  a  decimal. 
Usually,  however,  the  fraction  must  be  changed  to  higher 
terms,  but  always  to  a  fraction  having  a  decimal  denominator. 
What  is  a  decimal  denominator  ?     (See  No.  2.) 

Be  careful,  after  you  have  changed  to  a  fraction  with  a 
decimal  denominator  and  then  have  written  the  numerator 
of  this  fraction  for  the  decimal,  to  make  as. many  decimal 
places  as  there  are  ciphers  in  the  denominator.  Suppose 
you  have  the  fraction,  y^-J-g- ;  make  the  three  decimal  places 
by  writing,  point,  nought,  one,  seven,  .017. 

4.  [Change  to  higher  terms  and  then  to  decimals.] 

1^        -        .     1^        -        .     Therefore    ^^  x  ^  _  85  _  ., 
20x?-100      20x5-100      ^ '"'""*'''"'  20^-100-^^- 

Why  must  you  multiply  the  numerator  by  same  number 
by  which  you  multiply  the  denominator  ? 


DECIMALS  137 

18        = 18        = Therefore     1^><^ 

250  X?     1000      250x4     1000  '  250x4 

=  -^  =  .072. 
1000 

2  0"'   2  0"'   2  0'   2  0'   2"0'  2"0'   20"'    5  0'    5  0'    5  0'   5  0'   2^70"'   2  5  0"'  "^0  0'    12^' 

J  8         2  2         3J         5  2         34 
12  5'    12  5'    12^'    12  5'    12  5' 

[Sometimes  the  multiplier  is  a  mixed  number.] 

i-J-  9  9  9 

30x3i~100~'   40x2i~100~'    8x?~1000~' 

S~'    8~"    8~' 

190 

1.  What  is  a  decimal  ? 

2.  What  is  a  decimal  denominator  ? 

3.  What  is  a  decimal  system  ? 

4.  What  must  be  observed  in  writing  fractions  to  add  or 
subtract  ? 

5.  What  is  the  rule  for  pointing  off  the  sum  ? 

6.  What  is  the  rule  for  pointing  off  the  difference,  or 
remainder  ? 

7.  How  is  the  product  pointed  off  ? 

8.  How  is  the  quotient  pointed  off  ? 

9.  Moving  the  point  to  the  right  does  what  to  the  decimal? 

10.  Moving  the  point  to  the  left  does  what  to  the  decimal  ? 

11.  What  does  exceed  mean  ? 

12.  Make  a  list  of  as  many  cautions  concerning  decimals 
as  you  can. 


138  ARITHMETIC   WITHOUT  A  PENCIL 

13.  Read : 

.08,    .270275,    .0075,  .00015,  .017,  1.33J,   .06J,  150.015, 
.14 2 ,  25.0025. 

14.  Read  as  decimals : 

11312^412345735      J-        9        1        1J.4 

2?  :j^  f?  J^   5'    5'  ^'    8"'  "S"'   ■§■'  ¥'  ¥'   t'  TO'  TO'   10"'  TO"'  "5  0'  2^'  2 "5' 

2inr'  5"o 0'  10' 

15.  Read  as  common  fractions  in  lowest  terms  : 

.5,  .4,  .75,  .25,  .50,  .125,  .625,  1.75,  5.25,  .85,  7.05,  -95, 
.065,  .0046,  11.875,  .121,  .375. 

191 

Here  are  some  other  decimals  which  you  must  use  so  often 
that  you  should  learn  their  equivalent  common  forms. 

1.  .8Si=i        .66f=t 

Multiply  these  numbers  by  .33 J  and  by  .66J: 

24       60     150       27      120       69       165        36  300  18 

90      42       27       51      399      48         30        45  96  78 

330       20       39       84      240     600       180        57  21  54 

900     150     480     576      213     195     1200     1500  2400  1800 

2.  .16f=l        .83i=f 

Multiply  by  .16f: 

24   36   18   54   240   60   600    48    84   480 
96  150  120   72   360  240   300    90    78   270 
900  330   30  576   180   42  1200  2400 


28  42  7 
364  777  637 
140  1400  2100 


3.  .14f=i 

Multiply  by  .14|-: 

35   21   70   84 

14   91 

6 

56   98  350  700 

840  560 

140 

581  420  630  294 

854  427 

448 

DECIMALS 

139 

4. 

Multiply  by  .11-1  (i): 

2T 

18  210  549  1800   45 

54 

180 

648 

•2700 

63 

90  540  828  4500   81 

99 

900 

999 

1080 

36 

72  720  558  9000  549 

630 

6300 

369 

5. 

Multiply  by  .9J^(J^): 

55 

77   22  550   132   33 

6Q 

44 

330 

148 

88 

99  121  440  1100 

6.  Find  .081  (_!_)  and  .16f  (1)  of  these  numbers: 

72  600     1200     24     20     200     2000 

108  360    3000     12    18    180     1800 

84  240     8400     96    30    300     30000 

36  120    4800    132    25    250     2500 

192 

1.  .12iis  whatpartof  .25?     .37J?    .50?    .621?    .871? 

2.  .371  is  what  part  of  .50  ?  .621  ?  .871  ?  What  decimal  ? 

3.  .081  is  what  part  of  .I6f?  .331?  .66f?  Whatdecimal? 

4.  .16|  is  what  part  of  .331  ?     .66f  ?     What  decimal  ? 

5.  .33 J  is  what  part  of  .66^?     What  decimal? 

6.  .371  is  what  part  of  .871  ?     What  decimal  ? 

7.  .621  is  what  part  of  .871  ?     What  decimal? 

8.  .25  is  what  part  of  .5  ?     What  decimal  ? 

9.  .12 J  is  what  part  of  .5  ?     What  decimal  ? 
10.    .16|  is  what  part  of  .831  ?     What  decimal  ? 

193 

1.  What  is  .75  of  $24?   Of  140?  Of  $.120?  .25  of  $1.60? 
Of $80? 

2.  What  is  .66f  of  $60  ?     Of  60  acres  ?    Of  6  acres  ?    Of 
1100? 


140  ARITHMETIC   WITHOUT   A  PENCIL 

3.  125  is  .5  of  what  ?     Is  .25  of  what  ?     Is  .05  of  what  ? 

4.  15  is  .121  of  what  ?    12  is  .121  of  what  ?    .75  of  what  ? 

5.  15  is  what  decimal  of  45  ?     Of  60?    Of  75?    Of  150  ? 

6.  25  is  what  decimal  of  75  ?    Of  50  ?    Of  100  ?    Of  250  ? 

7.  I  owned  40  acres  of  land  and  sold  .25  of  it.     How 
many  acres  did  I  sell  ? 

8.  A  merchant  bought  cloth  at  f  5  per  yard  and  sold  it 
so  as  to  gain  i  1.     What  decimal  of  the  cost  did  he  gain  ? 

9.  A  commission  merchant  charged  me  .11  of  the  money 
for  collecting  $  100.     How  many  dollars  did  he  charge  ? 

10.  I  gained  1 7  on  the  sale  of  a  cow.     This  was  .14^  of 
what  she  cost  me.     What  did  she  cost  ? 

11.  A  hardware  merchant  sold  basins  for  60  cents,  which 
was  .66|-  of  the  cost.     What  was  the  cost? 

12.  I  owned  .75  of  a  mine.     I  sold  .5  of  the  mine  to  one 
man  and  .05  of  it  to  another.     What  did  I  still  own  ? 

13.  I  owned  .75  of  a  mine  and  sold  .5  of  my  share.     What 
part  of  the  mine  did  I  sell  ? 

14.  Otis  had  15  pigeons.     He  sold  .33J-  of  them.     How 
many  did  he  sell  ? 

15.  Jack   bought   15   hens,    which  were    .6   of   what   he 
already  had.     How  many  had  he  at  first  ? 

16.  Lois  hemmed  9  yards  last  week.     To-day  she  hemmed 
.33 J  as  much.     How  much  did  she  hem  to-day  ? 

17.  25  miles  is  .5  of  the  distance  from  Mary's  home  to 
the  city.     How  far  is  it  to  the  city  ? 

18.  .11^  of  36  is  .5  of  what  number  ? 


DECIMALS  141 

19.  I  bought  three  yards  of  ribbon  at  f  .05.  This  was  .25 
of  my  entire  bill.     What  was  my  bill  ? 

20.  Milton  bought  a  bicycle  for  $  40.  When  he  has  paid 
i  30  he  will  have  paid  what  decimal  part  of  the  price  ? 

21.  A  man  owns  .5  of  a  pasture  and  sells  .1  of  his  share. 
What  part  of  the  pasture  does  he  sell  ? 

22.  What  is  .01  of  i 90?  .01  of  1900?  .01  of  $9?  Of 
9  bushels  ? 

23.  What  is  .1  of  $90?   .2of|90?    .3of|90?    .3ofi9? 

24.  What  is   the   quotient  of   57.5  divided   by. 5?      Of 

100-r-.5? 

25.  What  is  the  product  of  .7x.3?  .8x.9?  .8x9.? 
.8x.09?     .08X.09? 

26.  .875  is  equal  to  what  comndon  fraction  ?  .625?  .125? 
.66f? 

27.  11  is  what  decimal  of  3  ?   21  of  10?   3  of  9?   15  of  20? 

28.  .25  of  20  +  .75  of  16  are  how  many  ? 

29.  .33 J  of  36  is  .5  of  what  number? 

30.  Add  :    .2  of  20  and  .5  of  30  and  .121  of  64. 

194 

After  reading  and  working  as  here  given,  re-read,  if  pos- 
sible, substituting  common  fractions  for  decimals  and  deci- 
mals for  common  fractions. 

1.  A  man  has  a  journey  of  75  miles  to  perform.  When 
he  has  gone  -^^  of  it  and  |  of  it,  how  many  miles  has  he  still 
to  go  ?     What  part  has  he  still  to  go  ? 

2.  A  boy  spent  |-  of  his  money  and  had  $  3  left.  How 
much  had  he  at  first  ? 


142  ARITHMETIC   WITHOUT   A   PENCIL 

3.  Amos  spent  |  of  his  money  and  J-  of  it  and  then  he 
had  f  7  left.     How  much  had  he  at  first  ? 

4.  Arnold  spent  |^  of  |  of  his  money  and  had  $  10  left. 
How  much  money  had  he  at  first  ? 

5.  There  were  48  pupils  in  a  class.    3  of  them  were  absent. 
What  part  was  absent  ? 

6.  .75  of  a  class  of  44  were  promoted.     How  many  were 
not  promoted  ? 

7.  .25  feet  are  what  decimal  part  of  100  feet  ? 

8.  1  foot  is  what  decimal  of  a  yard  ?     Of  2  yards  ? 

9.  A  newsboy  buys  papers  for  3  cents  and  sells  them  for 
6  cents.     His  gain  is  what  part  of  the  cost  ? 

10.  What  will  ^  of  40  yards  of  cloth  cost  at  $  |  per  yard  ? 

11.  What  will  f  of  a  yard  of  silk  cost  at  $  1^  per  yard  ? 

12.  If  it  takes  5  men  3  days  to  do  a  piece  of  work,  how 
long  will  it  take  6  men  to  do  it  ? 

13.  If  it  takes  8  men  3  days  to  do  a  piece  of  work,  how 
many  men  could  do  it  in  4  days  ? 

14.  Lee  chopped  2^  cords  of  wood  last  week,  which  was  .5 
of  what  he  chopped  the  week  before.  How  much  did  he 
chop  in  the  two  weeks  ? 

15.  When  eggs  are  f  ^  per  dozen,  how  many  dozen  can  be 
had  for  $1.50? 

16.  If  10  acres  of  land  produce  15  tons  of  hay,  how  much 
will  24  acres  produce  ? 

17.  If  12  acres  produce  20  tons  of  hay,  how  many  acres 
will  it  take  to  produce  30  tons  ? 

18.  At  f  ^  apiece,  what  will  25  chairs  cost  ? 


DECIMALS  143 

19.  At   |.66|  apiece,  how  many  chairs  can    be  bought 

for  112? 

20.  Tom  spent  ^  of  his  money  for  stamps,  10  cents  for 
paper,  and  had  ^  of  it  left.  How  much  did  he  spend  for 
stamps  ? 

21.  John  can  do  a  piece  of  work  in  6  days.  Jack  can  do  it 
in  8  days.  How  long  will  it  take  the  two  working  together 
to  do  it  ? 

22.  Mary  and  Louise  working  together  can  make  a  dress 
in  4  days.  Mary  can  do  it  alone  in  6  days.  How  many 
days  would  it  take  Louise  alone  to  make  it  ? 

23.  In  a  box  were  100  oranges.  .08  of  them  decayed. 
How  many  sound  ones  were  left  ? 

24.  1^  of  the  distance  around  a  field  is  35  rods.  What  is 
the  distance  around  it  ? 

25.  A  man  having  spent  .66|  of  his  money  has  f  50  left. 
What  had  he  at  first  ? 

26.  At  1 1  a  yard,  how  many  yards  of  silk  will  cost  $  1 J  ? 

27.  A  wheel  in  turning  round  goes  IJ  yards.  How  many 
times  must  it  turn  to  go  5  yards  ? 

28.  16f  is  what  part  of  100  ? 

29.  WhatisjoflOO?     J^?     ^\?     1?     J?     I?     1?     f? 

30.  40  pounds  is  .25  of  a  certain  man's  weight.  What  is 
his  weight  ? 

31.  If  I  buy  cloth  at  $  .25  and  sell  it  at  .2  advance  on  the 
cost,  for  what  do  I  sell  it  ? 

32.  A  can  do  a  piece  of  work  in  2  days,  B  in  3  days,  C  in 
4  days.     How  long  will  it  take  the  three  together  ? 


144  ARITHMETIC   WITHOUT  A   PENCIL 

33.  A  can  do  a  piece  of  work  in  10  hours,  B  in  12  hours, 
C  in  20  hours.     How  long  will  it  take  the  three  together  ? 

34.  A  can  do  a  piece  of  work  in  3  weeks,  B  in  5  weeks, 
and  C  in  6  weeks.  How  long  will  it  take  A,  B,  and  C 
together  ? 

35.  I  spent  I  of  my  money  for  board,  J  for  traveling  ex- 
penses, and  then  had  $  55  left.     How  much  had  I  at  first  ? 

36.  Max  paid  |-  of  his  week's  wages  for  board  and  put  J  of 
it  in  the  bank.  He  had  i  2  still  in  his  purse.  What  were 
his  wages  ? 

37.  In  a  class  of  32  pupils  .12^  were  absent.  How  many 
were  present  ? 

38.  Last  evening  I  read  120  pages  in  a  book  of  360  pages. 
What  decimal  part  of  the  book  did  I  read  ? 

39.  371  is  what  part  of  100  ?     831  is  what  part  of  100  ? 

40.  At  the  rate  of  3  for  a  quarter,  how  many  ball  bats  can 
be  bought  for  1 31? 

41.  Two  men  start  from  a  certain  point  and  travel  in  op- 
posite directions,  one  at  the  rate  of  5J  miles  per  hour,  the 
other  at  the  rate  of  7|-  miles  per  hour.  How  long  will  it 
take  them  to  be  85  miles  apart  ? 

42.  Joel  had  $  5J  left  after  paying  three  bills,  respectively, 

'$  71,  $  .75,  and  $  3J.     How  much  had  he  before  paying  his 
bills  ? 

43.  It  costs  20  cents  per  box  to  import  foreign  oranges. 
What  will  it  cost  to  import  150  boxes  ? 

44.  A  collector  receives  .05  of  all  the  money  he  collects. 
How  much  must  he  collect  to  earn  $  15  ? 


DECIMALS  146 

45.  .16|  of  $  72  is  what  decimal  of  $  120  ?  What  is  .12| 
of  84? 

46.  8  X  J  of  40  is  .8  of  what  ?     What  is  .66f  of  1 20  ? 

47.  3.5  X. 5 +  .3=?     $7.50  is  .331  of  what? 

48.  What  is  .001  of  $25?  |1.25  is  what  decimal  of 
$5.00? 

49.  What  is  .Of  of  30  ?     What  is  .5  of  .16|  of  75  ? 

50.  The  difference  between  2  cents  and  3  cents  is  what 
decimal  of  2  cents  ? 

51.  If  A's  money  is  .5  of  B's,  B's  is  how  many  times  A's  ? 

52.  If  my  money  is  .25  of  yours,  yours  is  how  many  times 
mine  ? 

53.  A's  farm  is  .66^  times  as  large  as  B's  ;  then  B's  is  how 
many  times  as  large  as  A's  ? 

54.  John  is  .75  as  heavy  as  his  father.  His  father  is  how 
many  times  as  heavy  as  he  ? 

55.  My  age  is  .4  of  my  mother's.  Her  age  is  how  many 
times  mine  ?. 

56.  Divide  1  by  |.  Divide  1  by  |.  Divide  1  by  |. 
Divide  1  by  ^. 

57.  1-^1  =  ?  l-i5  =  ?  l-f  =  ?  1-H.25=?  l-^.5=? 
1^.75==? 

58.  Here  is  a  new  word  :  re-cip'-ro-eal.  The  reciprocal  of 
any  number  is  the  quotient  obtained  by  dividing  1  by  that 
number. 

59.  Find  the  reciprocal  of  each  of  the  following  : 

2,  10,  17,  20,  25,  100,  75,  85,  88,  37,  45,  18,  24  ;  i  J,  |,  |,  |, 

h  h  t\'  1^'  i  ih  If  U^  ih  ^r  f ;  n^  H^  H^  H^  li  H^  n^ 

21  2|,  3f ,  31  3f ,  1^. 


146  ARITHMETIC   WITHOUT   A   PENCIL 

195 

1.  If  a  yard  of  ribbon  costs  12^  cents,  how  many  yards 
can  be  bought  f  or  f  5  ? 

2.  At  16|-  cents  per  yard,  how  many  yards  of  muslin  will 
cost  14? 

3.  At  8^  cents  a  pound,  what  will  24  pounds  of  cheese 
cost  ? 

4.  If  a  man's  wages  are  $  33|-  a  week,  how  long  must  he 
work  to  earn  I  300  ? 

5.  At  il.25  a  gallon,  what  will  10  gallons  of  ice  cream 
cost  ? 

6.  At  8.80  a  pound,  how  many  pounds  of  tea  will  cost 
$20? 

7.  If  8  yards  of  lace  cost  $  1.00,  what  will  10  yards  cost  ? 

8.  If  2  yards  of  gingham  cost  66^  cents,  how  many  yards 
can  be  bought  for  $  12  ? 

9.  If  17  half -pints  of  cream  cost  $.85,  what  will  13  pints 
cost  ? 

10.  If  5  collars  cost  $.75,  what  will  12  collars  cost? 

11.  If  12  felt  hats  cost  $  30,  what  will  15  hats  cost  ? 

12.  If  12  hats  cost  $  30,  how  many  can  be  bought  for  $40  ? 

13.  If  15  yd.  of   broadcloth   cost  $  75,  how  many  yards 
can  be  bought  for  $  125  ? 

14.  If  7|  cords  of  wood  cost  $37.50,  what  will  14  cords 
cost? 

15.  If  9 J  bushels  of  potatoes  cost  $  5,  how  many  bushels 
will  $  1  buy  ? 

16.  If  15  men  do  a  piece  of  work  in  12  da.,  how  long  will 
it  take  4  men  to  do  it  ? 


DECIMALS  147 

17.  If  10  men  do  a  piece  of  work  in  6  days,  how  many 
men  will  it  take  to  do  it  in  15  days  ? 

18.  If  a  post  5  ft.  high  casts  a  shadow  T|  ft.  long,  how 
long  a  shadow  will  a  post  11  ft.  high  cast  ? 

19.  If  a  post  3  ft.  high  casts  a  shadow  5  ft.  long,  how  high 
is  a  church  steeple  whose  shadow  is  125  ft.  long  ? 

20.  If  25  gallons  of  water  last  a  certain  number  of  men 
7  days,  how  long  will  35  gallons  last  ? 

21.  If  5  bbl.  of  flour  last  3  men  a  certain  time,  how  many 
barrels  will  be  required  for  100  men  for  the  same  time  ? 

22.  How  many  feet  of  wire  can  you  buy  for  $  16  if  you 
can  get  2  yards  for  f  .16|  ? 

23.  At  the  rate  of  4  for  5  cents,  how  many  lemons  can 
you  buy  for  31^  cents  ? 

24.  At  the  rate  of  3  for  10  cents,  how  many  newspapers 
can  a  boy  buy  for  $  1.00  ? 

25.  If  ^  the  value  of  a  ship  is  $  3600,  what  is  |  of  its 
value  ? 

26.  If  $  81  is  Y^Q  of  the  cost  of  a  certain  cow,  what  is  ^  of 
the  cost  ? 

27.  I  sold  an  acre  of  land  for  $  75,  which  was  |  of  the  cost. 
If  I  had  sold  it  for  $  125,  the  selling  price  would  have  been 
what  part  of  the  cost  ? 

28.  A  dozen  chairs  cost  $  25.  What  would  9  chairs  cost 
at  the  same  rate  ? 

29.  If  -^  of  a  yard  of  velvet  cost  83.50,  what  will  IJ  yards 
cost? 

30.  If  lumber  costs  $  35  per  M.,  how  many  feet  cost  f  28  ? 


148  ARITHIVIETIC   WITHOUT   A  PENCIL 

31.  After  I  had  spent  .33^  of  my  money  and  then  .16 J  of 
it  and  then  .25  of  it,  I  had  $7  left.  How  much  had  I  at 
first? 

32.  I  of  my  money  is  |  of  Paul's.  J  of  his  money  is  $  15. 
How  much  has  each  ? 

33.  At  the  rate  of  15  pounds  for  f  1  J,  how  many  pounds 
of  raisins  can  be  had  in  exchange  for  5  dozen  eggs  at  22  cents  ? 

34.  A  farmer's  barley  crop  was  120  bushels.  If  he  puts 
it  into  sacks  holding  2|-  bushels,  what  will  the  sacks  cost  at 
10  cents  apiece  ? 

35.  If  it  takes  12  sheets  of  tin  24  in.  wide  to  line  a  tank, 
how  many  sheets  30  in.  wide  will  be  needed  to  line  another 
of  same  size? 

36.  How  many  men  will  dig  24  feet  of  ditch  in  the  same 
time  it  takes  3  men  to  dig  18  feet  ?     In  half  the  time  ? 

37.  How  many  men  will  dig  45  feet  of  ditch  in  the  same 
time  it  takes  5  men  to  dig  25  feet  ?     In  one-third  the  time  ? 

38.  If  8  men  dig  32  feet  of  ditch  in  a  given  time,  how 
many  feet  will  11  men  dig  in  the  same  time  ? 

39.  One-half  of  the  distance  around  a  certain  square  field 
is  24  rods.     What  is  its  area  ? 

40.  What  is  the  field  worth  at  |100  per  acre  ? 

41.  Divide  $75  between  two  boys,  giving  one  boy  50  cents 
when  you  give  the  other  25  cents.  How  much  will  each 
receive  ? 

42.  Divide  75  into  two  parts  having  the  ratio  of  2  to  1. 
\_Iiatio,  relation.] 

43.  A  publisher  receives  orders  for  900,  1500,  and  2100 
copies  of  a  book  respectively.     He  has  only  3000  copies  in 


DENOMINATE   NUMBERS  149 

stock.      If   his   3   customers   share   in   proportion   to  their 
orders,  how  many  books  will  each  receive  ? 

44.  A  man  divides  $111  among  his  three  sons  according 
to  their  ages,  which  are  10,  12,  and  15  years  respectively. 
How  many  dollars  does  each  receive  ? 

45.  Three  men  together  own  an  oil  well.  The  profits  are 
$150  per  day.  How  much  should  each  receive  if  they  put 
into  it  respectively  the  sums  of  1 500,  $3500,  and  $1000  ? 

196 

1.  How  many  feet  in  7  yd.  ?     7-|- yd.  ?     101  yd.  ?     8.33J 
yd.  ?     1.66|  yd.  ? 

2.  How  many  inches  in  51  ft.  ?     61ft.?    8Jft.?    831ft.? 
2.081ft.? 

3.  1^  yd.  are  how  many  feet?     Inches?     7.75  yd.  are 
how  many  inches  ? 

4.  15  in.  are  how  many  feet  ?     What  part  of  a  yard  ? 
What  decimal  of  a  yard  ?     Of  2  yd.  ? 

5.  9  in.  are  what  part  of  a  yard  ?     What  decimal  of  1  yd.  ? 
Of  3  yd.? 

6.  ^  yd.  are  how  many  inches  ?    Feet  ?     What  part  of 
5  ft.  ?     What  decimal  of  30  in.  ? 

7.  .5  of  a  yard  is  how  many  feet?     Inches?     .75  of  a 
yard  is  how  many  feet  ? 

8.  1.5  yd.  are  how  many  feet?     Inches?     1.25  yd.  are 
what  part  of  5  yd.  ? 

9.  .33 J  yd.  are  how  many  inches?     Feet?     .66|  yd.  are 
how  many  inches  ? 

10.  .16|  yd.  are  how  many  inches?  100  in.  are  how 
many  yards  ? 


150  ARITHMETIC    WITHOUT  A   PENCIL 

11.  24  in.  are  what  part  of  a  yard  ?    Of  2  yd.  ?    Of  3  yd.  ? 

12.  2  rods  are  how  many  yards?  Feet?  10  rods  are 
how  many  feet  ?     Yards  ? 

13.  Change  -Od^j  rd.  to  yards.     To  feet.     To  inches. 

14.  160  rods  are  what  part  of  a  mile  ?     What  decimal  ? 

15.  What  part  of  a  mile  are  10  rods  ?  20  rods  ?  32  rods  ? 
100  rods  ? 

16.  .25  of  a  mile  is  how  many  rods  ?     .125  mi.  ? 

17.  A  boy  runs  10  rd.  a  minute.  How  long  will  it  take 
him  to  run  a  mile  ? 

18.  A  kite  tail  is  10  yd.  2  ft.  long.  How  many  yards 
long  is  it  ?  How  many  feet  long  ?  Is  it  more  or  less  than 
2  rd.  long  ? 

19.  A  certain  wheel  goes  4  ft.  10  in.  in  each  revolution. 
What  is  the  length  in  yards  around  it  ? 

20.  What  will  1-|  miles  of  fence  at  $1J  per  rod  cost? 
1.621- miles? 

21.  The  distance  around  a  certain  building  is  100  rods. 
How  many  paces  of  3  feet  will  a  man  take  in  going  around  it  ? 

22.  1  mile  and  50  rods  are  how  many  rods?  1.9  mi.  are 
how  many  rods  ? 

23.  .75  of  a  mile  is  how  many  rods  ?     .37 J  mi.  ?     .625  mi.  ? 

24.  .87 J  of  a  mile  are  how  many  rods  ? 

25.  120  rods  are  what  part  of  a  mile  ?     What  decimal  ? 

26.  How  many  miles  around  a  field  that  is  300  rods  long 
and  200  rods  wide  ? 

27.  The  distance  around  a  certain  square  field  is  800  rods. 
What  part  of  a  mile  is  one  side  ? 


DENOMINATE  NUMBERS  151 

28.  10  rods  are  how  many  yards  ?     How  many  feet  ? 

29.  J  rd.  is  how  many  yards  ?     How  many  feet  ? 

30.  How  many  feet  of  picture  molding  will  be  needed  to 
fit  a  room  17  ft.  wide  and  20  ft.  long  ? 

31.  J  of  a  mile  is  what  decimal  of  a  mile  ? 

32.  .375  of  a  mile  is  what  fraction  of  a  mile  ? 

33.  I  of  a  mile  is  what  decimal  of  a  mile  ? 

34.  5  yards  are  what  part  of  a  mile  ? 

35.  A  certain  street  is  66  ft.  wide.  What  part  of  a  mile 
is  this  ? 

36.  At  a  certain  time  a  monument  25  feet  high  cast  a 
shadow  5  yards  long.  What  part  of  the  height  of  the 
monument  is  the  length  of  its  shadow? 

37.  At  the  same  time  a  certain  church  steeple  casts  a 
shadow  30  feet  long.     Fow  high  is  the  steeple  ? 

38.  How  many  rods  of  iron  rails  are  used  in  laying  10 
miles  of  railroad  track  ? 

39.  How  many  feet  of  rabbit  wire  are  used  in  inclosing  a 
lot  50  feet  wide  and  150  feet  deep  ?     How  many  yards  ? 

40.  5    yd.  -  I  yd.  =  what?         7|^f  =  ?  7.5^.75  =  ? 

41.  7    yd.-^f  yd.  =  what?       10|-f  =  ?        10.5^.75  =  ? 


42.   10    yd. -f  yd.  =  what?       17   -f=?        17.    ^.75 


.  ^o  = 


_9 


43.  41  yd.  ^  I  yd.  =  what  ?         3f^|  =  ?  4.5 

44.  5J  yd.  ^  I  yd.  =  what  ?       15   ^|=?        15.    ^.75  =  ? 

45.  How  many  strips  of  carpet  f  of  a  yard  wide  will  be 
required  to  cover  the  floor  of  a  room  12  ft.  wide  if  the  strips 
are  laid  lengthwise  ? 


152  ARITHMETIC    WITHOUT   A   PENCIL 

46.  How  many  if  the  room  is  27  ft.  wide  ? 

47.  What  are  11  strips  of  carpet,  each  containing  5  yards, 
worth  at  $  1  per  yard  ? 

48.  What  is  the  cost  of  3  strips  of  carpet,  each  strip  being 
21  feet  long,  at  11.50  per  yard  ? 

49.  How  long  is  a  stone  wall  inclosing  a  field  16  rods 
wide  and  20  rods  long  ?     What  decimal  part  of  a  mile  long  ? 

50.  How  many  yards  in  a  mile  ?     In  two  miles  ? 

51.  How  many  feet  in  a  mile  ?     In  three  miles  ? 

52.  How  many  rods  in  a  mile  ?     How  many  chains  in  a 
mile  ?     (4  rd.  =  1  chain.) 

53.  How  many  rods  in  a  chain  ?     How  many  feet  in  a 
rod  ?     Then,  how  many  feet  in  a  chain  ? 

54.  How  many  links  in  a  rod  ?     How  many  links  in  a 
chain  ? 

55.  1  chain  is  how  many  links  ?     Rods  ?     Feet  ?     Yards  ? 

56.  A  chain  can  be  laid  twice  across  a  certain  lot.     How 
wide  is  the  lot  ? 

57.  How  many  steps  of  24  inches  will  you  take  in  march- 
ing the  length  of  a  chain  ? 

58.  What  decimal  of  a  mile  are  50  ch.  ?     60  ch.  ?     70  ch.  ? 
30  ch.  ? 

59.  60  chains  is  f  of  the  distance  around  a  certain  field. 
What  is  the  distance  around  it  ? 

60.  What  part  of  a  chain  are  72  links  ?     85  links  ? 

61.  How  many  chains  in  1760  yards  ? 

62.  How  many  chains  in  5280  feet  ? 

63.  How  many  links  in  10  chains  ? 


DENOMINATE   NUMBERS  153 

64.  How  many  feet  in  10  chains  ? 

65.  6,5  cli.  are  how  many  links  ? 

66.  8.75  ch.  are  how  many  links? 

67.  5.25  ch.  are  how  many  links? 

68.  125  1.  are  how  many  chains  ? 

69.  1000 1.  are  how  many  chains  ? 

70.  6Q  ft.  are  how  many  links  ? 

71.  27  inches  are  .  75  of  how  many  inches  ? 

72.  30  inches  are  .66|-  of  how  many  inches  ? 

73.  5 J  yards  are  .33 J  of  how  many  yards  ? 

74.  85  links  are  what  part  of  100  links  ? 

75.  100  rods  are  .83^  of  how  many  rods  ? 

76.  150  rods  are  what  part  of  a  mile  ? 

77.  60  feet  are  what  decimal  of  a  chain  ? 

78.  3|-  yards  are  what  part  of  a  rod  ? 

79.  20  links  are  what  decimal  of  a  rod  ? 

80.  1 J  rods  are  what  part  of  a  chain  ? 

81.  How  far  around  a  field  twice  as  long  as  wide  if  it  is 
20  rods  wide  ? 

82.  How  far  around  a  field  .5  as  wide  as  long  if  it  is  10 
rods  wide  ? 

83.  My  garden  is  50  feet  long  and  .8  as  wide.  How  much 
fence  will  be  required  to  inclose  it  on  the  two  sides  and  one 
end  ? 

84.  Frances  is  4  feet  8  inches  tall,  and  her  father  is  1.121 
times  as  tall.     How  tall  is  he  ? 

85.  I  measured  a  stake  and  its  shadow,  finding  the  shadow 
to  be  .83^  as  long  as  the  stake  was  tall.  How  high  is  a 
building  whose  shadow  at  the  same  time  was  60  feet  long  ? 


154  ARITHMETIC   WITHOUT   A   PENCIL 

197 

1.  My  table  is  3  feet  wide  and  4  feet  long.     How  many 
square  feet  in  it  ? 

2.  How  many  square  feet  in  a  table  21  feet  wide  and 
4  feet  long?     1.75  ft.  by  4  ft.? 

3.  What  is  the  surface  of  a  table  4  ft.  wide  and  6.25  ft. 
long  ? 

4.  What  is  the  surface  of  the  floor  of  a  room  10  ft.  wide 
and  15  ft.  long  ? 

5.  What  is  the  surface  of  a  floor  12  ft.  by  20  ft.?     12  ft. 
by  20.33^  ft.? 

6.  How  many  square  feet  in  the  ceiling  of  each  room 
above  mentioned  ? 

7.  What  is  the  ceiling  of  a  room  141  ft.  by  16  ft.  ? 

8.  What  is  the  surface  of  one  wall  of  a  room  10  ft.  high, 
if  the  wall  is  14  ft.  long  ? 

9.  Of  opposite  walls  in  the  above-mentioned  room  ? 

10.  A  certain  room  is  12  ft.  square.  If  the  walls  were 
straightened  out  into  one  wall,  how  long  would  it  be  ?  In 
other  words,  how  far  is  it  around  a  room  10  ft.  square  ? 
12  ft.  square  ?     20.5  ft.  square? 

11.  How  far  is  it  around  a  room  12.33|-  feet  wide  and 
15  feet  long  ?  If  the  walls  in  this  room  are  10  feet  high, 
how  many  square  feet  in  them  ? 

12.  What  is  the  surface  of  the  walls  of  a  room  10  ft.  wide 
and  12  ft.  long,  if  the  room  is  10  ft.  high  ? 

13.  A  certain  room  is  15  ft.  square.  It  is  11  ft.  high. 
What  is  the  area  of  its  walls  ?     Of  its  ceiling? 


DENOMINATE  NUMBERS  155 

14.  A  certain  square  room  has  81  square  feet  in  its  ceiling. 
What  is  the  size  of  the  room  ? 

15.  The  area  of  a  certain  table  is  40  sq.  ft.  It  is  4  ft. 
wide.     How  long  is  it  ? 

16.  If  the  area  of  a  billboard  is  240  sq.  ft.  and  it  is  20  ft. 
long,  how  wide  is  it  ? 

17.  The  area  of  a  given  rectangle  is  200  sq.  ft.  It  is 
twice  as  long  as  wide.  Draw  a  diagram  of  it  and  find  its 
dimensions.  \_Rectangle^  a  figure  having  four  sides  and  four 
square  corners.] 

18.  Another  rectangle  contains  8  sq.  ft.  It  is  half  as  wide 
as  long.     Draw  a  diagram  and  find  dimensions. 

19.  How  many  square  inches  in  a  square  foot  ?  In  2  sq. 
ft.  ?     In  IJ  sq.  ft.  ? 

20.  J  sq.  ft.  is  how  many  square  inches?  .25  sq.  ft.  is 
how  many  square  inches  ? 

21.  10  sq.  ft.  are  how  many  square  inches?  10.75  sq.  ft. 
are  how  many  square  inches  ? 

22.  84  sq.  in.  are  what  part  of  a  square  foot  ?  72  sq.  in. 
are  what  decimal  of  a  square  foot  ? 

23.  10  sq.  yd.  are  how  many  square  feet  ? 

24.  7  sq.  ft.  are  what  part  of  a  square  yard  ? 

25.  5  sq.  ft.  are  what  decimal  of  1  sq.  yd.  ? 

26.  .44|^  sq.  yd.  is  how  many  square  feet? 

27.  Change  .62 J  sq.  yd.  to  the  fraction  of  a  square  yard. 

28.  How  many  square  yards  in  1  sq.  rd.  ?     In  2  ? 

29.  90.75  sq.  yd.  are  how>many  square  rods? 

30.  ^  sq.  rd.  is  how  many  square  yards  ? 


156  ARITHMETIC   WITHOUT   A   PENCIL 

31.  One  acre  is  equal  to  how  many  square  rods  ? 

32.  A  man  owned  10  acres  of  land  and  sold  ^  oiit.  How 
many  square  rods  did  he  sell  ? 

33.  A  lot  10  rods  by  12  rods  contains  what  part  of  an 
acre  ? 

34.  .87 J  of  an  acre  is  how  many  square  rods  ? 

35.  How  far  must  you  walk  to  walk  along  one  side  of  a 
section  of  land  ? 

36.  How  far  to  walk  around  it  if  it  be  square  ? 

37.  How  many  acres  in  a  section,  or  square  mile  ? 

38.  Draw  a  map  of  a  section  of  land  and  divide  it  into 
quarters.  What  will  the  east  J  of  the  northeast  i  sell  for 
at  $  100  per  acre  ? 

39.  How  many  square  feet  in  a  gable  roof  whose  ridge- 
pole is  20  ft.  and  whose  rafters  are  15  ft.  ? 

40.  What  is  the  area  of  the  bottom  of  a  box  3  ft.  wide 
and  5  ft.  long  ?     What  is  the  area  of  the  cover  ? 

41.  What  is  the  area  of  one  of  the  sides  of  a  box  2  ft.  deep 
and  5  ft.  long  ?     What  is  the  area  of  the  opposite  side  ? 

42.  What  is  the  area  of  the  end  of  a  box  2  ft.  deep  and 
3  ft.  wide  ?     What  is  the  area  of  the  opposite  side  ? 

43.  What  is  the  outside  surface  of  a  box  2  ft.  deep,  3  ft. 
wide,  and  5  ft.  long  ? 

44.  What  is  the  outside  surface  of  a  box  1  ft.  deep,  3  ft. 
wide,  and  4  ft.  long  ? 

45.  Draw  a  box,  mark  dimensions,  and  find  area. 

46.  How  many  sides  has  every  cube  or  other  rectangular 
solid  ?  t 


DENOMINATE  NUMBERS  167 

47.  Find  the  area  of  a  block  of  stone  4  ft.  thick,  5  ft. 
wide,  and  10  ft.  long. 

48.  The  inside  measurements  of  a  covered  rectangular 
tank  are  3  ft.,  4  ft.,  and  6  ft.  How  many  square  feet  of 
zinc  will  be  required  to  line  it  ? 

49.  The  area  of  one  of  the  sides  of  a  cubical  box  is  25 
sq.  ft.     What  are  the  dimensions  ? 

50.  The  area  of  a  certain  cubical  block  of  stone  is  294  sq. 
ft.     What  are  the  dimensions  ? 

51.  One  square  mile  is  how  many  acres  ? 

52.  What  is  another  name  for  a  square  mile  ? 

53.  ^  sq.  mi.  is  how  many  acres  ? 

54.  If  an  acre  be  divided  into  10  equal  parts,  one  part  is  a 
square  chain.     How  many  acres  in  a  square  chain  ? 


55.    How  many  square  chains  in  1  A.  ?     In  li^  A 


? 


56.  In  a  quarter-section  how  many  square  chains  ? 

57.  A  man  owned  a  quarter-section  of  land.  He  sold  5 
square  chains.     How  many  acres  had  he  left  ? 

58.  What  are  2  sq.  ch.  of  land  worth  at  $  100  per  acre  ? 

59.  Draw  a  diagram  of  a  field  4  rd.  square.  What  is  its 
area  ?  Draw  another  diagram  of  a  field  each  of  whose  sides 
is  1  ch.  What  is  its  area?  What  is  the  relative  size  of 
these  two  fields  ? 

60.  1  sq.  ch.  is  how  many  square  rods  ? 

61.  1  A.  is  how  many  square  chains  ? 

1  sq.  ch.  is  how  many  square  rods  ? 
Then  1  A.  is  how  many  square  rods  ? 

62.  How  many  square  rods  in  an  acre  ? 


158  ARITHMETIC   WITHOUT   A   PENCIL 

63.    What  is  an  acre  of  land  worth  at  $  100  per  square  rod  ? 

€4.   25  times  25  is  what? 

€5.    1  rod  is  how  many  links  ? 

Then  1  sq.  rd.  is  how  many  square  links  ? 

€6.    125  sq.  1.  are  what  decimal  of  1  sq.  rd.  ? 

€7.    How  many  square  links  in  1  sq.  rd.  ? 

€8.    10  sq.  rd.  500  sq.  1.  are  how  many  square  links  ? 

69.  Draw  a  diagram  to  illustrate  :  A  surveyor  laid  his 
chain  5  times  to  the  north  of  a  given  point,  then  4  times  to 
the  east,  then  6  times  to  the  south,  then  4  times  to  the  west, 
then  to  point  of  starting.  How  many  times  did  he  lay  the 
chain  in  all  ? 

70.  A  man  owned  |^  of  a  quarter-section  of  land.     He  sold 

1  sq.  ch.     What  part  of  his  land  did  he  sell  ? 

71.  At  $  1^  per  acre,  what  does  a  quarter-section  of  land 
cost? 

198 

1.  A  certain  block  of  stone  is  2  ft.  wide  and  3  ft.  long. 
What  is  the  area  of  one  of  its  sides  ?  It  is  one  foot  thick, 
therefore  its  solid  contents  is  6  cu.  ft.  Another  stone  of 
equal  size  is  placed  upon  it.  Now,  there  are  how  many 
cubic  feet  in  the  two  stones  ? 

A  third  stone  is  equal  in  size  to  these  two.  Its  length 
and  breadth  are  the  same  as  the  length  and  breadth  of  each 
of  the  others,  2  ft.  by  3  ft.  Its  thickness  is  the  same  as 
both  the  others,  2  ft.  Therefore  its  solid  contents  is  as 
much  as  the  sum  of  the  other  two.  How  much  is  that  ? 
Hence,  a  block  of  stone  2  ft.  by  2  ft.   by  3  ft.   contains 

2  X  2  X  3  cu.  ft.,  or  12  cu.  ft. 


DENOMINATE  NUMBERS  159 

2.  How  many  cubic  feet  in  a  block  5  ft.  long,  3  ft.  wide, 
and  2  ft.  thick  ? 

3.  Find  the  contents  of  a  rectangular  solid  IJ  ft.  thick, 
4  ft.  wide,  and  10  ft.  long. 

4.  In  a  block  of  wood  6  ft.  long,  3  ft.  wide,  and  3|  ft- 
thick,  are  how  many  cubic  feet  ? 

5.  A  certain  solid  is  1  ft.  wide,  3|-  it,  long,  and  2  ft. 
thick.     What  is  its  contents  ? 

6.  What  is  the  contents  of  a  brick  8  in.  long,  and  5  in. 
wide,  and  2^  in.  thick  ? 

7.  How  many  cubic  feet  in  a  solid  15  in.  by  1  ft.  by  5  ft.? 

8.  In  a  pile  of  wood  8  ft.  long,  4  ft.  wide,  and  4  ft.  high, 
how  many  cubic  feet  ?     This  is  one  cord. 

9.  How  many  cubic  feet  in  one  cord  ? 

10.  2  cords  are  how  many  cubic  feet  ? 

11.  1^  cords  are  how  many  cubic  feet?     1.25  cords  are 
how  many  cubic  feet.? 

12.  -|  cord  is  how  many  cubic  feet?     .625  cord  is  how 
many  cubic  feet  ? 

13.  A  pile  of  wood  4  ft.  long,  2  ft.  wide,  and  4  ft.  high, 
contains  what  part  of  a  cord  ?     What  decimal  of  1  cd.  ? 

14.  1280  cu.  ft.  are  how  many  cords  ? 

15.  How  many  cords  of  wood  will  just  fill  a  wagon-box 
8  ft.  long,  4  ft.  wide,  and  6  ft.  deep  ? 

16.  How  many  cubic  feet  of  water  will  a  tank  8  ft.  by 
4  ft.  by  6  ft.  hold  ? 

17.  How  many  cubic  feet  of  air  in  a  room  10  ft.  high, 
10  ft.  wide,  and  12  ft.  long  ? 


160  ARITHMETIC   WITHOUT   A  PENCIL 

18.  How  many  cubic  feet  of  masonry  in  a  wall  3  ft.  high, 

3  ft.  wide,  and  30  ft.  long  ? 

19.  3  ft.  =  1  yd.       (3x3  =  9)      9  sq.  ft.  =  1  sq.  yd. 
(3  X  3  X  3  =  27)     27  cu.  ft.  =  1  cu.  yd. 

270  cu.  ft.  are  how  many  cubic  yards  ? 

20.  How  many  cubic  yards  in  81  cu.  ft.  ? 

21.  5  cu.  yd.  are  how  many  cubic  feet  ? 

22.  What  part  of  108  cu.  ft.  is  1  cu.  yd.  ?    What  decimal  ? 

23.  12  in.  =  1  ft.    (12  X  12  =  144)    144  sq.  in.  =  1  sq.  ft. 
(12  X  12  X  12  =  1728)    1728  cu.  in.  =  1  cu.  ft. 

24.  1  CU.  ft.  is  how  many  cubic  inches  ? 

25.  864  cu.  in.  are  what  decimal  of  a  cubic  foot  ? 

26.  How   many  cubic   feet   of   earth  were   excavated  in 
digging  a  ditch  l^-  ft.  wide,  1^  ft.  deep,  and  50  ft.  long  ? 

27.  .121   of   a   cubic   foot   is   how   many   cubic    inches  ? 
,11^  cu.  ft.  is  how  many  cubic  inches  ? 

28.  The  contents  of  a  certain  stone  is  320  cu.  ft.     It  is 

4  ft.  thick  and  8  ft.  wide.     How  long  is  it  ? 

29.  Change  .375  of  a  cord  to  cubic  feet. 

30.  If  a  cubic  foot  of  wood  weigh  20  lbs.,  how  much  will 
weigh  540  lbs.  ? 

31.  Some  units  of  measurement  compared  : 
Unit  of  length,  1  foot. 

Unit  of  area,  1  foot  by  1  foot,  or  1  square  foot. 
Unit  of  contents,  1  foot  by  1  foot  by  1  foot,  or  1  cubic  foot. 
Unit  of  lumber  measure,  1  foot  by  1  foot  by  1  inch^  or 
1  board  foot. 

How  many  board  feet  in  a  cubic  foot  ? 


DENOMINATE   NUMBERS  161 

32.  How  many  board  feet  in  a  board  1  in.  thick,  1  ft.  wide, 
and  12  ft.  long  ? 

33.  How  many  board  feet  in  2  such  boards  ? 

34.  How  many  board   feet   in  a  plank  2  in.  thick,  1  ft. 
wide,  and  12  ft.  long  ?     In  2  ? 

35.  How  many  board  feet  in  100  one-inch  boards  10  inches 
wide  and  18  feet  long  ? 

36.  How  many  board  feet  in  a  joist  4  in.  wide,  4  in.  thick, 
and  12  ft.  long  ? 

37.  How  many  feet  in  a  timber  4  in.  square  and  18  ft.  long  ? 

38.  How  many  M.  are  2375  ft.?     500  ft.?     10,325  ft.? 
9250  ft.?    4250  ft.?     9500  ft.?     3333J  ft.  ? 

39.  Find  cost  at  §20  per  M.:  5000  ft.,  10,250  ft.,  9500  ft. 

40.  Find  cost  at  $24  per  M.:  33331  ft.,  5375  ft.,  2625  ft. 

41.  Find  cost  at  1 30  per  M. :  20,000  ft.,  100,000  ft.,  750  ft. 

42.  Find  average  width  of  tapering  boards  whose  ends  are 
respectively : 

8  inches  and  12  inches.         8  inches  and    9  inches. 

9  inches  and  15  inches.         4  inches  and    5  inches. 
3  inches  and    4  inches.         7  inches  and  11  inches. 

10  inches  and  12  inches.         4  inches  and    7  inches. 
7  inches  and    9  inches.         9  inches  and  11  inches. 

199 

1.  1  gallon  and  three  quarts  are  how  many  quarts  ? 

2.  1  gal.  3  qt.  1  pt.  are  how  many  pints  ? 

3.  Same  are  how  many  quarts  ? 

4.  Same  are  how  many  gallons  ? 


162  ARITHMETIC   WITHOUT   A  PENCIL 

5.  How  many  quarts  in  a  barrel  ? 

6.  2  bbl.  are  how  many  quarts  ? 

7.  A  milkman  has  a  5-gallon  can  full  of  milk  which  he 
leaves  to  customers  who  take  1  quart  each.  How  many 
customers  will  it  supply  and  how  much  is  it  worth  at  7  cents 
a  quar J.  ? 

8.  How  many  pint  bottles  will  be  required  to  hold  12| 
gallons  of  oil  ? 

9.  In  ^  bbl.  how  many  quarts  ? 

10.  From  a  cask  containing  28  gallons,  5  quarts  leaked  out. 
What  part  of  the  contents  of  the  cask  was  lost  ? 

11.  What  was  the  leakage  worth  at  80  cents  per  gallon  ? 

12.  What  is  the  contents  in  cubic  inches  of  a  gallon  ?  (231 
cu.  in.)     Of  2  gal.?     Of  10  ?     Of  100? 

13.  How  many  cubic  inches  in  a  quart  ? 

14.  How  many  half -pint  bottles  can  be  filled  from  a  gallon 
and  d,  half  ? 

15.  Which  is  more  and  how  much ;  Jg  gallon  or  ^  pint  ? 

16.  Change  3  qt.  1  pt.  to  the  decimal  of  a  gallon. 

17.  .375  gal.  is  how  many  pints  ? 

200 

1.  How  many  ounces  in  1  pound  ?     In  2  ? 

2.  240  oz.  are  how  many  pounds  ? 

3.  2  oz.  are  what  part  of  a  pound  ? 

4.  .87|^  lb.  is  how  many  ounces?     .6211b.? 

5.  40  pounds  is  .8  of  all  I  can  lift.  How  many  pounds 
can  I  lift  '^ 


DENOMINATE  NUMBERS  163 

6.  150  pounds  is  1^  times  what  my  brother  can  lift. 
How  much  can  he  lift  ? 

7.  48  lbs.  is  I  of  my  weight.     How  much  do  I  weigh  ? 

8.  80  lbs.  15  oz.  (average  weight  of  3  persons). 
3 

(whole  weight  of  3  persons). 

9.  5)320  lbs.  10  oz.  (whole  weight  of  5  children). 

(average  weight). 

10.  A  certain  four-horse  team  weighs   4448  lbs.  12  oz. 
What  is  the  average  weight  of  the  horses? 

11.  Change  5276  lbs.  to  tons. 

12.  Change  6495  lbs.  to  tons. 

13.  .25  T.  is  how  many  pounds  ? 

14.  How  many  centals  in  3J  tons  ?     How  many  pounds  ? 

15.  What  are  2J  centals  of  dried  fish  worth  at  5  cents  a 
pound  ? 

16.  16|-  lbs.  are  what  fraction  of  a  cental  ? 

17.  What  is  the  cost  of  |  of  a  cental  of  flour  at  1^  cents 
per  pound  ? 

18.  How  many  pounds  of  butter  at  35  cents  a  pound  are 
worth  as  much  as  5|  gal.  milk  at  10  cents  a  quart  ? 

19.  In  1  ton  how  many  ounces  ? 

20.  What  decimal  of  a  ton  are  750  pounds  ? 

21.  250  tons  are  .83^  of  how  many  tons  ? 

22.  How  many  ounces  in  a  pound  Troy  ? 

23.  How  many  pennyweights  in  1  oz.  ?     In  2  ? 

24.  I  of  an  ounce  is  J  of  how  many  pennyweights  ? 

25.  2  lbs.  4  oz.  are  how  many  ounces  ?     Pounds  ? 


164  ARITHMETIC   WITHOUT   A   PENCIL 

26.  10  oz.  18  pwt.  are  how  many  pennyweights  ?  Ounces  ? 

27.  32  pwt.  are  .66^  of  how  many  pennyweights  ? 

28.  1  lb.  6  oz.  6  pwt.  are  how  many  pennyweights  ? 
Ounces  ?     Pounds  ? 

29.  1  pwt.  is  how  many  grains?     3  pwt.?     5? 

30.  18  grains  are  what  part  of  a  pennyweight  ? 

31.  What  decimal  of  a  pennyweight  are  9  grains  ? 
'32.   Express  10  pwt.  15  gr.  as  grains. 

33.  Express  same  as  pennyweights. 

34.  If  a  pennyweight  of  gold  is  worth  a  dollar,  how  many 
grains  are  worth  25  cents  ? 

PBROENTAGB 
201 

Does  i=-j5^=.5?  Do  we  change  the  value  of  .5  if  we 
annex  a  cipher,  writing  it  .50?  Are  .50  and  -f^  equal  in 
value?  Here  is  another  way  of  writing  y^^:  50^.  Notice 
how  the  100  in  the  denominator  is  used  in  the  sign  Jo.  50^ 
is  read,  50  per  cent. 

Note  that  1  =  35^  =  . 5  =  .50  =  ^5_0o  =  50/o. 

Now  you  must  learn  the  same  about  many  fractions,  and 
must  finally  shorten  all,  as  1=50^,  since  the  sign  f)  is  equal 
to  the  denominator  100, 

1.    25^  =  ^2^Q,  reduced  to  lowest  terms,  equals  :|. 
75^= TOT 


u 

u 

a 

(( 

a 

? 

a 

u 

a 

u 

u 

? 

u 

a 

(• 

(.i 

(( 

? 

PERCENTAGE  165 

2.  60fc  =  j%%  =  i. 

70fo     8O/0     90fo    40fo     30^     65f     95^     85^    55^    45fo 
35/o       5^      4^       8fo       370       2/0       170       Qfo      If)      9/0 

3.  Change  these  to  fractions  in  lowest  terms : 

15/0     16fo     24:fo     28fo     36fo     44fo     88/0     66fo    99^    71fo 
mjo     56^     84^     76fo     48^     96fo     94^     86^    22/o    34^ 

4.  121^  =  ?  371^  =  ?  62ifo  =  ?  87-1-5^=? 

5.  What  is  25  fo  of  40  ?      60  ?      24  ?      36  ?      1000  ?      8  ? 
1?    1200?     2000?     50? 

6.  What  is  50/0  of  30?      100?      1000?      12?      25?     8? 
7?     44?    4000?     1500?     80? 

7.  What  is  75^  of  36?     20?     100?     1000?     10?     50? 

80?     24?     2?     16?     48?     96? 

« 

8.  Find   121/0,  37ifo,  621^,  and  87l/o  of  each  of  the 
following  numbers : 

40,  64,  24,  96,  80,  72,  88,  8,  16,  32,  56,  800,  160,  7200, 
240,  2400,  4000,  880,  8000,  1600,  720,  120,  1200,  440,  816, 
152,  728,  960. 

9.  33i/o  =  ?       66|fo  =  ? 

10.  Take  33|^^  and  66|^  of  each  of  these  numbers : 

30,  60,  90,  120,  150,  180,  18,  15,  21,  210,  24,  27,  36,  33, 
480,  3000,  6000,  51,  81,  6,  900,  72,  240,  1200,  150,  1500, 
96,  9600,  100. 

11.  Change  these  to  common  fractions  in  lowest  terms : 
20^     40%     60^     80fo     30%     50%     70%     90%       1%      2% 

3%   4%   5%   6%   7%   8%   9%  10%  11%  12% 


166  ARITHMETIC   WITHOUT   A  PENCIL 

12.  What  is : 

709feof40?  25^  of  48?  33^^  of  60?  66f/oof24? 

12i^of24?  87i^of40?  37i^of72?  4^of500? 

I^of700?  5^of200?  62ifoof480?  33Jfoof240? 

66|^of240?  4^  of  200?  37ifoof64? 

13.  Memorize  all  that  have  been  given  and  these,  which 
you  may  also  prove  : 

14.  Comparing  the  following  with  the  above,  state  what 
each  is  when  written  as  a  common  fraction : 

22ffo       44|^       55f^       77|fo       88f/o       18^\^       45-^^^ 
21j\fo     363-^^     831^0       28^^       131^       ISlfo 

15.  Find  142^  of  21,  35,  42,  84,  70,  700,  100,  50,  14,  140, 
35,  3500. 


16. 

17. 

18. 

19. 

20. 

162^  Of: 

831^  of: 

142^  of: 

111^  Of: 

9^1^^  of 

6 

30 

28 

36 

44 

36 

60 

21 

90 

66 

60 

54 

35 

54 

121 

6Q 

72 

14 

72 

33 

96 

180 

42 

18 

55 

12 

18 

49 

81 

88 

42 

600 

70 

180 

77 

120 

420 

77 

1800 

1100 

240 

1200 

84 

27 

220 

300 

10 

140 

270 

10 

PERCENTAGE 

1( 

21. 

22. 

23. 

24. 

25. 

Slfoof: 

^fou 

6i/oof: 

Ifoi: 

1/oof: 

1200 

15 

3200 

500 

2000 

600 

30 

320 

700 

5500 

36 

QO 

32 

240 

1728 

60 

75  ■ 

16 

375 

6600 

6000 

150 

80 

498 

3000 

72 

3000 

800 

673 

5760 

96 

600 

96 

537 

5250 

144 

90 

24 

284 

4782 

5T6 

120 

64 

715 

6840 

240 

1200 

48 

800 

2350 

26. 

27. 

28. 

29. 

30. 

1/oof: 

1/oof: 

J/oof: 

\foU 

If  oil 

^25 

15.00 

1300 

1300 

11.00 

75 

10.00 

400 

600 

2.00 

32 

7.00 

800 

1200 

10.00 

14 

7.50 

1000 

120 

5.00 

20 

2.50 

1200 

12 

4.00 

35 

4.50 

1500 

60 

100.00 

63 

^ 

1728 

84 

400.00 

87 

H 

5840 

51 

200.00 

45 

9.75 

3250 

990 

20.00 

16  3.375  72  180  2000.00 

31.  1^  of  1150,    i/oof|60,    Jo^of|75,     -jV/^  of  17.50, 
If  of  15.60. 

32.  ^/o  of  12.50,     ifoof.60,     jfoof$1400,     i/oof$810, 
ifoofi>1200. 

202 

1.  What  is  1  of  $200?  What  is  1 /oof  1200? 

2.  What  is  1  of  13.60?  What  is  ^^  of  83.60? 


168 


ARITHMETIC   WITHOUT   A   PENCIL 


3.  What  is  3^  of  1000  i 

4.  Whatis  Jof  24? 

5.  What  is  f  of  300  ? 

6.  What  is  I  of  120  ? 

7.  What  is  f  of  4000  ? 

8.  What  is  I- of  560  ? 

9.  What  is  y4_  of  44  ? 
10.  What  is  I  of  250  ? 


Whatis  J^^of  1000? 
What  is  ^fo  of  24? 
What  is  f/o  of  300? 
What  is  l/o  of  120? 
What  is  Ifo  of  4000? 
Whatis  Jfoof  560? 
What  is  ^4_/o  of  44? 
What  is  Ifo  of  250? 


It  is  important  to  note  how  much  the  sign  ^  affects  the 
value  of  any  number.  It  should  always  be  used  with  care, 
as  should  the  decimal  point. 


11. 

What] 

sl^of  40? 

What  is  .5fo  of  40? 

12. 

What! 

si^of  600? 

What  is  .25^  of  600? 

13. 

What] 

sf/oof  1000? 

What  is  .75fo  of  1000? 

14. 

What] 

IS  iV/o  of  50  ? 

What  is  .Ifo  of  50? 

15. 

What] 

sf/oof  25? 

What  is  .6^  of  25? 

16. 

What] 

s  .7^  of  $1400? 

$700?    170?    17?    $1000? 

17. 

What] 

Ls.l5foof  1600? 

What  is  15^0  of  $600? 

18. 

What  ] 

IS  11^  of  1000? 

What  is  1.5^  of  1000? 

19. 

What 

is  1|^  of  360? 

What  is  1|^  of  36? 

20. 

What] 

Ls  2.5^  of  100? 

What  is  25^  of  100? 

21. 

What] 

s  21^  of  68? 

Whatis2ifoof  680? 

22. 

What] 

Lsl^foof  200? 

What  is  1.25/0  of  200? 

23. 

What  ] 

Ls  100 /oof  200?' 

What  is  125  fo  of  200? 

24. 

What 

isl25foof  20? 

What  is  125/)  of  2? 

25. 

What 

IS  150^  of  1000? 

What  is  150/,  of  10? 

PERCENTAGE  169 

203 

1.  Often  it  is  necessary  to  change  a  common  fraction  to 
a  decimal  or  a  per  cent.  Some  fractions  should  be  memorized 
in  per  cents.  This  should  be  done  as  thoroughly  as  one 
learns  the  multiplication  table. 

Change  these  to  ^  from  memory  of  previous  lessons : 

h  h  f '  h  I'  h  h  I'  i'  6'  6'  h  h  h  to'>  A'  tV'  t^o'  iSc  i^' 
1    JL    i_ 1 

20'  25'   50'    1000* 

2.  One  will  need  to  change  to  f)  other  fractions  than  those 
he  has  memorized,  so  he  must  learn  how  it  is  done.  Let  us 
take  I  to  change  to  ^. 

As  per  cent  means  hundredths,  changing  |^  to  ^  means 
changing  it  to  hundredths. 

I         = ,  therefore  l^^^^  =  ^  =  dO%. 

2x50     100'  2x50     100         ^ 

3.  What  must  each  of  the  following  denominators  be 
multiplied  by  to  make  them  100  ? 

h  h   sV'  2V'  2V  ^ 

4.  Remember,  if  you  would  not  change  the  value  of  a 
fraction,  you  must  perform  the  same  operation  upon  the 
numerator  that  you  do  upon  the  denominator. 

5.  Change  these  fractions  to  fo  :  (They  involve  a  multi- 
plier that  is  a  mixed  number.) 

T5x?  =  T"ro  =  -  16'  2 If'  TP  3  0'  IXT'  80'  16'  IT'  15^'  eO"'  Y%.Y'U'> 
90"'   1?'  15* 

6.  What  kind  of  a  multiplier  do  these  involve  ?  Change 
them  : 

20'0'xJ'    STTO'    6 "00"'    TO 0  0"'    4'0  0"'    "8 "00'    "TOlT'   1"©^'    3TD"'    TOO* 


170  ARITHMETIC   WITHOUT  A  PENCIL 

Read  as  fractions  in  lowest  terms  : 

7.  14f  fo,  20^,  25^,  mi%  37 J ^,  ^^%  15%  63%  33 J ^, 
111^. 

8.  12J/0,  8^^,  9^^%  iq%  Ql%  61%  871/.,  621  fo,  3^,  1^. 

9.  45/0,  30/0,  55%  J-Q-fo,  .5/0,  .25/0,  1% 

Read  as  per  cent : 

10-     ^1    2"'   1'    5'    5'    6'   6'   h  ^'   12'  "S"'   "g^'  "9'  TT'  T'  T'S'   16'    3'   "3' 
TO'  ^IT'  2'5* 

^^-     "50'  IT'    lO"'  "^0'   3  0"'    6  0'  ¥0"'    3  0'   1"^"0'  T0"00"'  "SOT'  2"00''  ^0  0' 
3T0'  ¥00'  6  OT* 

12.  .5,  .25,  .75,  .6,  .12,  .61  .35,  .01, 1.2,  If,  2i  1.5,  IJ,  .375. 

13.  .625,  .125,  .875,  .005,  .0625,  .11111   .0909yi-,  4444|, 
.01125,  .015. 

14.  .0125,  .0175,  .001,  .0025. 


204 


i 


1.  5  is  what  part  of  15  ?     What  per  cent  ?     Of  20  ?   25  ? 
35  ?     50  ? 

2.  10  is  what  part  of  70  ?   What  per  cent  ?    Of  25  ?   80  ? 
16  ?     24  ? 

3.  12  is  what  part  of  96  ?    What  per  cent?     Of  18  ?   36? 
30  ?     100  ? 

4.  25  is  what  part  of  75  ?    What  per  cent  ?    Of  30  ?   45  ? 
60  ?     72  ? 

5.  30  is  what  part  of  60  ?    What  per  cent  ?    Of  40  ?    50  ? 
33  ?     36  ? 

6.  12  is  what  per  cent  of  48  ?    Of  72  ?  15  of  18  ?  20  of  24  ? 


PERCENTAGE  171 

7.  5  is  what  per  cent  of  55  ?   Of  40  ?  18  of  20  ?  33  of  44  ? 

8.  7  is  what  per  cent  of  56  ?   Of  63  ?  20  of  25  ?  24  of  25  ? 

9.  10  is  what  per  cent  of  90  ?  Of  300  ?  24  of  36  ?  30  of  75  ? 

10.  3  is  what  per  cent  of  300?  Of  3000  ?  5  of  35?  35  of  70  ? 

Note  that  these  are  examples  in  Division.      Re-read  as 
such ;  also  the  following  exercise. 

205 

1.  7  is  331^  of  what  ?  20^  of  what  ? 

2.  3  is  16|fo  of  what  ?  U^-fo  of  what  ? 

3.  56  is  871^  of  what  ?  66f  ^  of  what  ? 

4.  25  is  83 J  ^  of  what  ?  25  ^  of  what  ? 

5.  7  is  111  J^  of  what  ?  20  ^  of  what  ? 

6.  12  is  66|  f)  of  what  ?  50  ^  of  what  ? 

7.  15  is  60  ^  of  what  ?  50  ^  of  what  ? 

8.  27  is  75  f,  of  what  ?  142  ^^  of  what  ? 

9.  30  is  621 9^  of  what  ?  83i/o  of  what  ? 
10.  32  is  25  ^  of  what  ?  12i  fo  of  what  ? 

11.  24  is  75^  of  Avhat  ?  12.  35  is  83ifo  of  what  ? 
13.  35  is  621-^  of  what  ?  14.  36  is  60  fo  of  what  ? 
15.  45is  55ffo  of  what?  16.  49  is  87ifo  of  what ? 
17.  35  is  871 /o  of  what  ?  18.  30  is  371^  of  what  ? 
19  12  is  lllfo  of  what  ?  20.  84  is  77J^  of  what  ? 


172  ARITHMETIC   WITHOUT   A  PENCIL 

206 

1.  What  is  50^  of  $24 ?  2.  What  is  25^  of  |64  ? 

3.  What  is  33J^  of  27  acres?  4.  What  is  66|^  of  36  pounds? 
5.  What  is  75 fo  of  1000  miles  ?  6.  What  is  16f /o  of  30  miles? 
1.  What  is  20^  of  50  cents  ?  a  What  is  40^  of  75  gallons? 
9,  What  is  80  f  of  25  days  ?    10.  What  is  60  f  of  15  hours  ? 

Re-read,  using  fractions  instead  of  ^,  and  the  proper  sign 
instead  of  of. 

207 

12  is  what  per  cent  of  24  ? 

12  =  -i-f  =  1  of  24.     1  =  50  fo.     Therefore,  12  is  50^  of  24. 

1.  30  is  what  per  cent  of  75  ? 

2.  1750  is  what  per  cent  of  1 1000  ? 

3.  12  yards  are  what  per  cent  of  36  yds.  ? 

4.  16  cents  is  what  per  cent  of  24  cents  ? 

5.  8  20  is  what  per  cent  of  f  25  ? 

6.  2  cents  is  what  per  cent  of  4  cents  ? 

7.  30  pounds  is  what  part  of  50  lbs.  ? 

8.  25  cents  is  what  per  cent  of  fl  ? 

9.  12  acres  is  what  per  cent  of  30  acres  ? 
Re-read  the  above  as  fractions. 

208 

12  is  50^  of  what? 

50  fo  =  \.     12  is  1-  of  24.     Therefore,  12  is  50  fo  of  24.    • 

1.  15  is  331^0  of  what? 

2.  118  is  60^  of  what? 


PERCENTAGE  173 

3.  21  miles  is  75^  of  what? 

4.  8  oz.  is  80%  of  how  many  ? 

5.  20  is  66f%  of  what? 

6.  142  is  60%  of  how  many  dollars? 

7.  14  cents  is  40%  of  what  ? 

8.  11  is  20%  of  what? 

9.  17  isl6|%  of  what? 
Re-read  the  above  as  fractions. 


1.  A  man  owned  50  acres  of  land  and  sold  10  acres. 
What  per  cent  of  his  farm  did  he  sell? 

2.  John  has  $  30  in  the  bank.  Marion  has  16|%  as  much. 
How  much  has  Marion  ? 

3.  A  farmer  owned  a  quarter-section  of  land  and  sold 
75%  of  it.     How  much  did  he  sell  ? 

4.  I  sold  a  house  for  14000,  which  was  80%  of  the  cost. 
What  was  the  cost  ? 

5.  I  bought  a  house  for  84000  and  sold  it  for  80%  of  the 
cost.     For  what  did  I  sell  it  ? 

6.  A  newsboy  bought  papers  at  3  cents  apiece  and  sold 
them  for  5  cents  apiece.  How  much  did  he  gain  ?  What 
per  cent  of  the  cost  did  he  gain  ? 

7.  An  orchardist  planted  75  orange  trees  and  60%  as 
many  lemon  trees.     How  many  lemon  trees  did  he  plant  ? 

8.  In  a  battle  an  army  lost  6000  men,  which  was  25%  of 
the  number  of  men  engaged.  How  many  men  were  engaged 
in  the  battle  ? 

9.  A  merchant,  whose  income  is  $2000  per  year,  saves  all 
but  75%  of  it.     How  much  does  he  save  ? 


174  ARITHMETIC   WITHOUT   A  PENCIL 

10.  A  boy,  after  spending  QQ^%  of  his  money,  has  13.50 
left.     How  much  had  he  at  first  ? 

11.  From  a  bolt  of  cloth  15  yards  have  been  cut.  That 
wliich  remains  is  66  J  %  of  the  entire  piece.  How  many  yards 
in  the  entire  piece  ? 

12.  Lynn  has  175  in  the  bank;  Robert  has  40%  as  much, 
and  Robert's  money  is  60%  of  Harry's.  How  much  has 
Harry  ? 

13.  A  farmer  raised  72  bushels  of  oats,  which  was  75%  of 
his  crop  of  barley.  50%  of  his  crop  of  barley  was  equal  to 
his  crop  of  wheat.     How  many  bushels  of  wheat  did  he  raise  ? 

14.  I  sold  a  cow  for  112  more  than  she  cost,  which  was  a 
gain  of  25%  upon  the  cost.     What  was  the  cost  ? 

15.  A  man  traveled  3000  miles  last  month,  which  was  60% 
of  what  he  traveled  this  month.  How  much  did  he  travel 
this  month  ? 

16.  Maurice  spelled  96  words  correctly  in  an  examination  ; 
Arthur  spelled  75%  as  many,  and  Harry  spelled  75%  as  many 
as  Arthur.     How  many  did  Harry  spell  ? 

17.  A  man  paid  $55  for  a  watch  and  20%  as  much  for  a 
chain.     What  did  both  cost  ? 

18.  40%  of  20  is  16f  %  of  what  ? 

19.  75%  of  36  is  what  per  cent  of  81  ? 

20.  What  per  cent  of  48  is  66f  %  of  24  ? 

210 

1.  A  farm  sold  for  110,000,  which  was  62J%  of  what  the 
owner  asked  for  it.     What  did  he  ask  for  it  ? 

2.  A  house  that  cost  $1600  was  sold  for  12  J  %  more  than 
it  cost.     How  much  was  gained  ? 


PERCENTAGE  175 

3.  Frank  sold  his  bicycle  for  $15,  which  was  37^%  of 
what  it  cost  him.     What  did  it  cost  him  ? 

4.  After  spending  $  35  I  had  121%  of  my  money  left. 
How  much  had  I  at  first  ? 

5.  A  man  owned  one  section  of  land.  He  sold  87|%  of 
it.     How  many  acres  did  he  sell  ? 

6.  1 30  is  621%  of  the  cost  of  a  suit  of  clothes.  What  is 
the  cost  ? 

7.  A  merchant  marked  goods  at  $2.40  per  yard,  but  was 
obliged  to  sell  for  87 1%  of  the  marked  price.  For  what 
did  he  sell  ? 

8.  A  fruit  dealer  is  obliged  to  sell  a  certain  lot  of  berries 
at  5  cents  per  pound,  which  is  37|^%  less  than  cost.  What 
was  the  cost  ? 

9.  Mary  has  40  books  in  her  library.  Her  brother  has 
64  books.     Mary's  books  are  what  per  cent  of  her  brother's  ? 

10.    I  have  $1000  in  the  bank.     If  I  draw  out  $125,  what 
per  cent  of  my  money  do  I  draw  out  ? 

211 

1.  $85  was  70%  of  the  price  of  a  ticket  to  New  York. 
What  was  the  price  ? 

2.  30%  of  my  money  will  pay  half  the  price  of  a  ticket  to 
Chicago.  If  I  buy  the  ticket  and  have  $  40  left,  how  much 
ijioney  had  I  at  first  ? 

3.  In  a  box  there  are  150  oranges.  30%  of  them  are 
Valencias.  How  many  Valencia  oranges  were  there  in  the 
box? 

4.  An  agent  collected  $21  for  me.  If  I  pay  Kim  10%  of 
what  he  collects,  how  many  dollars  do  I  pay  him  ? 


176  ARITHMETIC   WITHOUT  A  PENCIL 

5.  A  collector  collected  a  certain  sum  of  money.  After 
keeping  10%  of  it  for  his  work,  he  paid  over  to  the  com- 
pany for  whom  he  collected  it  f  9000.  How  much  money 
did  he  collect  ? 

6.  For  every  $10  a  merchant  invested  in  business  he 
receives  an  income  of  $  9.  His  income  is  what  per  cent  of 
his  investment  ? 

7.  A  man  owed  a  bill  of  $  60.  He  drew  a  check  for  70% 
of  the  amount  and  paid  cash  for  the  rest.  How  much  cash 
did  he  pay  ? 

8.  30%  of  a  certain  bill  is  I  3.90.     What  is  the  bill  ? 

9.  After  selling  90%  of  his  load,  a  potato  vender  had 
13  bushels  left.  How  many  bushels  had  he  before  he  sold 
any? 

10.  A  man  sold  37|%  of  a  quarter-section  of  land,  which 
was  30%  of  all  the  land  he  owned.  How  many  acres  of  land 
did  he  own  before  he  sold  any  ? 

11.  Carl  won  in  a  race  of  300  rods.  This  was  what  per 
cent  of  a  mile  ? 

12.  The  number  of  soldiers  killed  in  a  certain  battle  was 
equal  to  8J%  of  those  engaged,  who  numbered  12,000  men. 
How  many  were  killed  ? 

13.  84  gallons  is  11^%  of  all  a  certain  tank  will  hold. 
What  will  it  hold  ?       . 

14.  A  certain  oil  tank  holds  882  gallons.  When  there 
are  98  gallons  in  it,  what  per  cent  full  is  it  ? 

15.  ^jj^  of  the  oranges  in  a  box  containing  110  oranges 
were  bad.     How  many  were  good  ? 

16.  What  is  18 1\^  of  72  ?     Of  720  ? 


PERCENTAGE  177 

17.  What  is  55^^  of  45  ?     Of  4.5  ? 

18.  In  a  certain  compound  are  7  oz.  of  peppermint,  which 
is  8^^  of  the  whole  mixture.  How  much  does  the  whole 
weigh  ? 

19.  If  it  takes  36,000  ft.  of  lumber  to  build  a  carriage 
house,  and  I  lack  8000  ft.,  what  per  cent  of  the  whole  do 
I  lack? 

20.  Sold  a  cow  for  $7  more  than  I  paid  for  her,  thereby 
gaining  S^fo.     For  what  did  I  sell  her  ? 

212 

(Gain  or  Loss  per  cent  is  reckoned  on  the  cost.) 

1.  Find  gain  or  loss  per  cent : 

Bought  for  2  cents,  sold  for  3  cents. 
Bought  for  3  cents,  sold  for  2  cents. 
Bought  for  2  cents,  sold  for  4  cents. 
Bought  for  4  cents,  sold  for  2  cents. 
Bought  for  1|  cents,  sold  for  2  cents. 
Bought  for  150,  sold  for  1 75. 
Bought  for  $15,  sold  for  $16. 
Bought  for  f  1000,  sold  for  $1125. 
Bought  for  11500,  sold  for  11575. 

2.  Find  gain  or  loss  : 

Cost: 

$25,  20^  gain  =  $?gain. 

150,  10^0  loss. 

72,  11-1^  loss. 

35,  14f  ^  gain. 

42,  16f  ^  gain. 


178  ARITHMETIC   WITHOUT   A   PENCIL 

3.  Find  gain  or  loss. 

Cost  : 

5  cents,  80^  gain  =  ?  cents  gain. 
15  cents,  6|^  gain. 
$1.00,  lOfo  loss. 
$1.25,  4^  loss. 
$1000,  \^  loss. 

4.  Find  cost : 

Gain,  $50,  or  50 /o. 
Gain,  $7,  or  12^^. 
Gain,  $3,  or  4 /o. 
Loss,  $100,  or  16|/o. 
Loss,  $1,  or  1^. 
Gain,  5  cents,  or  33|^^. 
Gain,  \\  cents,  or  75^. 
Loss,  $2,  or  100^. 
Gain,  %m,  or  %1\% 
Loss,  $12,  or  f  ^. 

5.  Find  selling  price  in  Nos.  2,  3,  and  4. 

6.  Find  cost : 

Selling  price,  125^;  gain,  $10. 
Selling  price,  116J^;  gain  50  centSc 
Selling  price,  114|^;  gain,  $6. 
Selling  price,  90  ^  ;  loss,  20  cents. 
Selling  price,  75 /o  ;  loss,  $300. 
Selling  price,  1371 /o;  gain,  $24. 
Selling  price,  102/o;  gain,  $5. 
Selling  price,  98^;  loss,  $5. 
Selling  price,  95^;  loss,  $1. 
Selling  price,  101^^;  gain,  $1.50. 


PERCENTAGE  179 

7.  Find  cost : 

Selling  price,  1.40;  gain,  331^. 
Selling  price,  $35;  gain,  16|/o. 
Selling  price,  1 120;  loss,  20^. 
Selling  price,  24  cents;  loss,  li^fo. 
Selling  price,  3  cents;  gain,  50 fo. 
Selling  price,  |110;  gain,  10^. 
Selling  price,  59  cents;  gain,  18^. 
Selling  price,  55  cents;  loss,  16|^. 
Selling  price,  99  cents;  loss,  1%. 
Selling  price,  5  cents  ;  gain,  100%. 

8.  Buying  at  the  rate  of  5  for  3  cents  and  selling  at  the 
rate  of  3  for  6  cents  will  give  what  per  cent  gain  ? 

9.  If  selling  at  62 J  cents  gives  a  loss  of  16|%,  would  a 
selling  price  of  80  cents  have  given  a  gain  or  loss,  and  what 
per  cent  ? 

10.    If  a  half -cent  gain  is  33  J  %  gain,  what  per  cent  gain 
would  one-third  cent  have  been  ? 


213 

1.  If  an  agent  charges  2%  commission  for  investing 
money,  what  is  his  commission  for  buying  flOO  worth  of 
goods  ?  What  do  the  -f  100  worth  of  goods  really  cost  the 
man  for  whom  they  are  bought  ? 

2.  An  agent  sells  $500  worth  of  goods  on  a  commission 
of  1%.  What  does  his  commission  amount  to  ?  What  does 
the  owner  of  the  goods  receive  ? 


180  ARITHMETIC   WITHOUT  A  PENCIL 

3.  Find  commission : 

Cost  of  goods,  ilOOO  ;  rate  of  commission,  1%. 
Cost  of  goods,  1124  ;  rate  of  commission,  2%. 
Cost  of  goods,  $250  ;  rate  of  commission,  1^%. 
Cost  of  goods,  17  cents  ;  rate  of  commission,  3%. 
Cost  of  goods,  $4000  ;  rate  of  commission,  25%. 

4.  Find  the  whole  cost  in  each  above  case. 

5.  Find  commission  : 

Selling  price,  $50  ;  rate  of  commission,  2^%. 
Selling  price,  37^^;  rate  of  commission,  33^%. 
Selling  price,  $1500  ;  rate  of  commission,  5%. 
Selling  price,  $10,000  ;  rate  of  commission,  3^%. 
Selling  price,  $72.25;  rate  of  commission,  2%. 

6.  Find  proceeds  in  each  case  in  No.  5.     \_Proeeeds^  what 
is  left  of  selling  "price  after  commission  is  taken  out.] 

7.  Find  commission : 

Money  collected,  $  25  ;  rate  of  commission,  1  % . 
Money  collected,  $800  ;  rate  of  commission,  12J%. 
Money  collected,  $625  ;  rate  of  commission,  10%. 
Money  collected,  $500  ;  rate  of  commission,  20%. 
Mone}^  collected,  $15  ;  rate  of  commission,  15%. 

8.  Find  proceeds  in  each  case  above. 

9.  Find  rate  of  commission  : 

Money  collected,  $  1000  ;  commission,  $  10. 
Money  collected,  $  250  ;  commission,  $  25. 
Money  invested,  $5400  ;  commission,  $27. 
Money  invested,  $22.50  ;  commission,  $2,50. 


PERCENTAGE  181 

Selling  price,  $20  ;  commission,  fl.OO. 
Selling  price,  16^  ;  commission,  Ip. 
Selling  price,  f  3.50  ;  commission,  |.50. 
Money  collected,  il890  ;  commission,  $2.10. 
Money  collected,  $  25  ;  commission,  25  ^. 
Money  invested,  f  750  ;  commission,  $  5. 

10.  Commission  at  2%  was  ilO.     Find  money  collected. 
Commission  at  20%  was  $2.50.     Find  money  collected. 
Commission  at  11^%  was  $50.     Find  money  collected. 
Commission  at  J%  was  $3.     Find  selling  price. 
Commission  at  6|%  was  $25.     Find  selling  price. 
Commission  at  6\%  was  $400.     Find  selling  price. 
Commission  at  8J^,  $7.     Find  cost. 

Commission  at  Ifo,  $17.25.     Find  cost. 
Commission  at  1 9^,  $  100.     Find  cost. 
Commission  at  35^,  $35.     Find  cost. 

11.  Whole  cost,  including  commission,  was  $52.50.     The 
commission  was  $2.50.     What  was  the  rate  ? 

12.  Whole  cost,  including  $5.25  commission,  was  $180.25. 
What  was  the  rate  of  commission  ? 

13.  Whole  cost,  including  $150  commission,  was  $5150. 
What  was  the  rate  of  commission  ? 

14.  Whole  cost,  including  20)^  commission,  was  $80.20. 
What  was  the  rate  of  commission  ? 

15.  Whole  cost,  including  $8  commission,  was  $80.    What 
was  the  rate  of  commission  ? 

16.  Whole    cost,   including    Ifo    commission,    was    $101. 
What  was  the  cost  of  goods  ?     The  commission  ? 


182  ARITHMETIC   WITHOUT   A   PENCIL 

17.  Whole  cost,  including  25^  commission,  was  1 312 J. 
What  was  the  cost  of  the  goods  ?     Commission  ? 

18.  Whole  cost,  including  ^fo  commission,  was  81005. 
Find  cost  of  goods  and  the  commission. 

19.  Whole  cost  of  goods  and  commission  was  $1262.50. 
Find  cost  of  each  if  the  commission  was  1  fo. 

20.  What  was  the  commission  at  3  ^  on  goods  whose  whole 
cost  was  1108.15? 

21.  Remittance,  14160;  commission,  4^.  Find  amount 
invested  in  goods.      [Remittance^  money  sent  to  agent.] 

22.  Remittance,  1151.50;  commission,  l^o.  Find  cost  of 
goods. 

23.  Remittance,  $201 ;  commission,!^.     Find  cost. 

24.  Proceeds  from  a  sale  were  $99;  commission  was  $1. 
What  was  the  selling  price  ? 

25.  Proceeds,  $140;  commission,  $10.  Find  rate  of 
commission. 

Proceeds,  15  j^;  commission,  1^.  Find  rate  of  commission. 
Proceeds,  $29;  commission,  $1.  Find  rate  of  commission. 
Proceeds,  $49  ;  commission,  $1.  Find  rate  of  commission. 
Proceeds,  $100  ;  commission,  $50.   Find  rate  of  commission. 

26.  Proceeds,  $  75 ;  commission,  25^.  Find  selling  price 
and  commission. 

Proceeds,  $80;  commission,  6J^.  Find  selling  price  and 
commission. 

Proceeds,  $297;  commission.  If).  Find  selling  price  and 
commission. 

Proceeds,  $1000;  commission,  ^^^f).  Find  selling  price 
and  commission. 

Proceeds,  11^;  commission,  8J-^.  Find  selling  price  and 
commission. 


PERCENTAGE  183 

27.  Selling  price,  1550;  proceeds,  f500.  Find  rate  of 
commission. 

Selling  price,  $480;  proceeds,  $450.  Find  rate  of  com- 
mission. 

Money  collected,  1 30;  proceeds,  $21.  Find  rate  of 
commission. 

Money  collected,  810,000;  proceeds,  18750.  Find  rate 
of  commission. 

Money  collected,  $960;  proceeds,  $864.  Find  rate  of 
commission. 

28.  Proceeds,  80  ^  ;  commission,  $7.     Find  selling  price. 
Proceeds,  87  J  ^  ;•  commission,  f  14.     Find  selling  price. 
Proceeds,  99^  ;  commission,  $50.     Find  selling  price. 
Proceeds,  99 J  ^  ;  commission,  $3.     Find  selling  price. 
Proceeds,  95^;  commission,  $100.     Find  selling  price. 

214 

1.  How  much  money  must  I  send  my  agent  so  that  he 
can  buy  $918  worth  of  goods,  if  he  charges  2%  commission? 

2.  If  I  send  my  agent,  who  charges  2%  commission,  $918 
with  which  to  buy  goods,  how  many  dollars'  worth  of  goods 
can  he  buy  ? 

3.  My  agent  sends  me  $450  as  my  proceeds  from  the  sale 
of  goods.  If  he  charges  10%  commission,  what  was  the  sell- 
ing price  ? 

4.  At  another  time  my  agent  sends  me  $630  as  my  pro- 
ceeds of  a  sale  amounting  to  $700.  What  was  his  per  cent 
commission  ? 

5.  If  an  agent's  commission  for  collecting  $200  is  $5, 
what  is  his  rate  of  commission  ? 


184  ARITHMETIC   WITHOUT   A  PENCIL 

6.  The  selling  price  of  a  mine  was  $  100,000.  What  was 
the  agent's  commission  at  3%  ? 

7.  The  rate  of  commission  allowed  for  selling  a  certain 
tract  of  land  was  1^%.  What  was  the  selling  price  if  the 
commission  amounted  to  13000  ? 

8.  A  commission  merchant  sells  oranges  at  $2  per  box 
on  a  commission  of  1%.  How  many  boxes  must  he  sell  to 
make  150? 

9.  A  book  agent  receives  $1.25  for  selling  a  |5  book. 
What  is  the  rate  of  commission  ? 

10.  After  retaining  his  commission  of  5%,  an  agent  sends 
1 475  to  the  firm  for  whom  he  is  selling  books.  How  many 
volumes  has  he  sold  if  the  books  sell  at  15  ? 

215 

1.  When  the  duty  on  glass  is  40  cents  per  pound,  what 
will  it  cost  to  import  400  pounds  ? 

2.  What  is  the  duty  on  500  gallons  imported  olives  at  2 
cents  per  quart  ? 

3.  A  tobacconist  imported  1000  lbs.  cigars,  paying  a  duty 
of  |>4.50  per  pound.     What  was  the  cost  of  importing  ? 

4.  A  merchant  paid  |330  import  duty  on  handkerchiefs 
at  55%  ad  valorem.  What  was  the  cost  of  the  goods  and 
duty  ?     [^Ad  valorem,  according  to  value.] 

5.  What  is  the  duty  on  a  bolt  of  cotton  cloth  48  in.  wide, 
60  yd.  in  the  bolt,  at  2i  ^  per  square  yard  ? 

6.  What  is  the  duty  on  plate  glass  for  a  window  10  ft. 
square  at  11  ^  per  square  foot  ? 

7.  A  dealer  in  firearms  imported  1500  worth  of  muskets 
at  a  duty  of  25%  ad  valorem.     What  was  the  duty  ? 


PERCENTAGE  185 

8.  What  is  the  cost  of  importing  600  sq.  yd.  Oriental 
carpet  at  a  duty  of  10  ^  per  square  yard  and  40%  ad  valorem  ? 

9.  An  importer  paid  a  specific  duty  of  #30  on  1000  lb. 
coffee.  What  was  the  duty  per  pound  ?  \_Specific^  according 
to  weight  or  measure.] 

10.  It  cost  $1000  to  import  a  certain  bill  of  firecrackers  at 
8  ^  per  pound  ?     How  many  pounds  were  imported  ? 

11.  Cotton-seed  oil  is  charged  an  import  duty  of  4  ^  per 
gallon.     What  will  it  cost  to  import  100  bbl.  ? 

12.  1  paid  8 180  ad  valorem  duty  on  $400  worth  of  opera 
glasses.     What  was  the  rate  ? 

13.  A  stationer  imported  100  great  gross  pens  at  a  duty  of 
12  ^  per  gross.     What  was  the  entire  duty  ? 

14.  A  dealer  imported  4800  lb.  barley  and  1120  lb.  corn. 
He  paid  a  duty  of  30  /  per  bushel  of  48  lb.  on  the  barley, 
and  of  15  ^  per  bushel  of  3Q  lb.  on  the  corn.  What  was  the 
entire  duty  ? 

15.  It  costs  2|  ^  per  pound  to  import  chocolate.  A  man 
who  paid  a  duty  of  #100  imported  how  many  pounds  ? 

16.  A  wine  merchant  imported  1500  doz.  bottles  of  wine, 
paying  a  duty  of  16000.     What  was  the  duty  per  dozen  ? 

17.  It  costs  50^  per  pound  to  import  peppermint  oil. 
How  much  will  cost  175.50  ? 

216 

1.  If  it  costs  me  $4.50  to  insure  my  household  goods  for 
$1500  for  one  year,  what  is  the  rate  of  premium  ? 

2.  I  value  my  .property  at  $5000.  An  insurance  company 
will  insure  it  for  80%  of  its  value,  at  2%  per  annum.  What 
will  the  insurance  cost  me  in  5  years  ? 


186  ARITHMETIC   WITHOUT   A  PENCIL 

3.  The  Equitable  Life  Insurance  Company  charges  m  , 
3^^  for  a  policy  of  i2000.     What  is  my  yearly  premium  ? 

4.  A  man  had  his  life  insured,  when  he  was  twenty-five 
years  old,  for  §5000,  paying  at  the  rate  of  $16.50  on  a  thou- 
sand yearly.  What  did  his  premium  amount  to  at  thirty- 
five  ? 

5.  A  merchant  insured  his  stock  for  112,250  at  Sfo. 
What  did  it  cost  him  ? 

6.  A  ship's  cargo  was  insured  for  §7000.  In  a  storm  | 
of  the  cargo  was  lost.  What  insurance  should  the  owner 
receive  ? 

7.  An  accident  insurance  company  charged  $50  for  a 
f2000  policy.     What  was  the  rate  charged? 

8.  The  contents  of  a  warehouse  were  insured  at  ^^fo. 
What  was  the  insurance  valuation  if  the  premium  amounted 
to  $240? 

9.  Insuring  my  house  for  -|  of  its  value  cost  me  $120  at 
S^  premium.  *  What  is  the  value  of  the  house  ? 

10.    What  will  it  cost  a  jeweler  to  insure  his  stock  for 
$290,000  at  1|-^  premium? 

217 

1.  The  tax  in  a  certain  town  is  20  cents  on  $100.  What 
is  tlie  rate  of  taxation  ? 

What  is  the  rate  when  the  tax  is : 

2.  5  mills  on  a  dollar  ?     15)^  on  $100?     28  An  $100? 

3.  18  An  $100?  3  mills  on  $1.00?  4  mills  on  $1.00  ? 
'       4.    7  mills  on  $1.00?     14  cents  on  $100?     22^  on  $100? 


PERCENTAGE 


187 


5.    How  many  cents  on  flOO  is  a  tax  of: 


?i 


?     2( 


?    1 


«/^?     2 


0  7^  •     12 


•     1 1  7^  •     3  0 


Yr  '    9r  '    ii 
[|f«=8*o-     ^t^  of  1100  =  $1  =  371  cents.] 

6.  How  many  mills  on  a  dollar  is  each  of  the  above  rates  ? 

[f  ^  =  rh'  ro-o  of  100^  =  1^-  I  of  10  mills  =  ^^  mills 
=  2f  mills,  8.002f.] 

7.  When  the  rate  of  taxation  is  1.002 J  on  |1,  what  tax 
does  a  man  who  owns  12000  worth  of  property  pay  ? 

8.  When  the  rate  is  25  cents  on  $100,  what  does  a  man 
who  owns  $10,000  worth  of  property  pay? 

9.  When  the  rate  is  24  cents  on  a  dollar,  what  is  a  man's 
tax  on  1500? 

10.  A  tax  of  15000  is  levied  on  the  property  in  a  certain 
county.  What  is  the  rate  if  the  property  is  valued  at 
$1,000,000? 

11.  What  is  the  value  of  the  property  in  a  town  upon 
which  a  tax  of  $1500  is  raised  at  20^  on  $  100  ? 

12.  A  certain  street  tax  for  grading,  paving,  curbing,  and 
side- walking  is  $4  per  front  foot.  What  does  a  man  pay  on 
a  lot  75  ft.  wide  ? 

218 

1.   When  par  value  is  $100,  what  is  the  market  value  of 
stock  selling  at : 

^Hfo  premium  ? 

2Sfc  premium  ? 

140^  premium  ? 

10^  discount? 

1  f)  discount  ? 

331 /o  discount? 

l^fo  discount? 


10^  premium? 
1  fo  premium  ? 

25^  premium  ? 
33-|9^  premium  ? 
12^^  premium  ? 
100^  premium  ? 

75^  premium  ? 


12i  fo  discount  ? 
25 fo  discount? 
40 fo  discount? 
I  fo  discount  ? 
20^  discount? 
11  f)  discount  ? 


188  ARITHMETIC    WITHOUT   A   PENCIL 

2.  When  par  value  is  f  100,  what  is  the  market  value  of 
stock  quoted  at  : 

88f?  79?  56^?  99?  66|? 

87  J?  84?  112?  95?  150? 

1031?  68?  621?  90?  190? 

159?  20?  240?  50?  175? 

3.  Which  of  the  above  are  at  a  premium  ? 

4.  At  a  par  value  of  $100,  what  is  the  amount  of 
money  received  upon  one  share  when  the  company  declares 
a  dividend  of  : 

6%?  4%?  31%?  10%?  5%?  2%?  3%?  51%?  1%?  |%? 

5.  At   a   par   value    of  $100,   what   dividend  has  been 
declared  when  a  stockholder  receives  on  each  share  : 
fl.OO?    $1.25?    $2.50?    $5.00?    $li?    $2^?    $3i?    $1|? 

6.  A  man  bought  stock  at  25%  premium.  What  interest 
on  his  investment  does  a  $  1.25  dividend  pay  ? 

7.  A  man  bought  stock  at  98.  What  interest  on  his 
investment  does  a  dividend  of  $1.96  pay? 

8.  A  man  bought  stock  at  20%  discount.  When  a  5% 
dividend  is  declared,  what  rate  of  interest  on  his  investment 
does  he  receive  ? 

9.  I  bought  stock  at  par.  It  paid  2%  on  my  investment. 
What  dividend  was  declared  ? 

10.  I  bought  stock,  par  value  $100,  at  $50.  The  first 
dividend  paid  10%  on  my  investment.  What  per  cent 
dividend  had  been  declared? 

11.  I  bought  stock,  par  value  $  100,  at  105.  It  paid  J% 
interest  on  my  money      What  dividend  was  that  ? 


PERCENTAGE  189 

12.  I  bought  stock  at  par  value,  $  100.  How  much  had  I 
to  pay  on  100  shares  when  an  assessment  of  1  %  was  levied  ? 

13.  I  bought  stock,  par  value  $  100,  at  75.  An  assessment 
of  3%  was  levied.  What  had  50  shares  cost  me  when  I  had 
paid  this  assessment  ? 

[Unless  otherwise  stated,  par  value  is  always  understood 
to  be  1100.] 

[Assessments  are  levied  on,  and  dividends  declared  on, 
Par  Value.] 

14.  When  a  2|%  dividend  is  declared,  how  much  should  I 
receive  on  1000  shares  ? 

15.  When  a  1%  assessment  is  levied,  how  much  must  the 
owner  of  500  shares  pay  ? 

16.  When  a  4%  dividend  was  declared  a  certain  stock- 
holder received  $  100.  How  many  shares  did  he  own  ? 
How  much  had  the  shares  cost  him  if  he  bought  them  at  80  ? 

17.  What  per  cent  on  his  investment  did  above  income 
pay? 

18.  A  broker  bought  stock  at  88  and  sold  at  100.  What 
did  he  make  on  75  shares  ? 

19.  A  broker  bought  stock  at  112  and  sold  at  99.  What 
did  he  lose  on  30  shares? 

20.  A  broker  bought  stock  at  75  and  sold  at  such  a  price 
that  he  made  f  500  on  100  shares.  At  what  price  did  he 
sell? 

219 

1.   What  is  1%  of  each  of  the  following  amounts  : 
$100?  12000?  11500?     11740?     |500?   $3000?   82700? 
$3270?     $600?  $4000?    $2400?  $1720?     $800?   $7000? 
$3500?  $5280?     $900?  $10,000?  $3600?   $8240? 


190  ARITHMETIC   WITHOUT   A   PENCIL 

2.  What  is  2%  of  each  of  the  above  ? 

3.  What  is  ^%  of  each  of  the  above  ? 

4.  On  May  1  I  hired  $100.     On  April  1  I  paid  it  back, 
and  beside,  1%  of  the  sum  for  its  use.     How  much  did  I  pay  ? 

5.  What  should  I  pay  at  |^%  a  month  for  the  use  of  $500 
for  two  months  ? 

6.  If  I  borrow  i600  for  3  months  at  1%  per  month,  how 
much  must  I  pay  when  I  pay  the  debt  ? 

7.  What  name  is  given  to  the  sum  of  money  paid  for  the 
use  of  money  ? 

8.  What  is  the  interest  on  $800  for  4  months  at  ^%  per 
month  ? 

9.  What  is  the  interest  on  $900  for  1  year  at  6%  per 
year  ?     For  6  months  ? 

10.  What  is  the  interest  on  $2000  for  1  year  and  6  months 
at  6  %  per  year  ? 

11.  What  is  the  interest  on  : 

$3000  for  2  yr.  at  6%  per  year? 
$4000  for  1  yr.  9  mo.  at  6%  per  year? 
$2500  for  1  yr.  3  mo.  at  6%  per  year  ? 
$1500  for  1  yr.  1  mo.  at  6%  per  year? 
$5000  for  5  yr.  at  6%  per  year  ? 

12.  What  is  the  amount  to  be  paid  in  each  case  above 
when  the  debt  is  paid  ? 

13.  A  man  borrowed  $1000  on  Jan.  1,  1900,  at  10%  per 
year.     What  is  the  amount  of  the  debt  due  on  Nov.  1, 1901  ? 

14.  Find  interest  on  : 

$1200  for  9  mo.  at  10%.     $1725  for  1  yr.  at  5%. 


PERCENTAGE  191 

15.  I  paid  $72  for  the  use  of  $1200  for  1  year.     What 
was  the  rate  of  interest  charged  ? 

16.  I  paid  'SlOO  for  the  use  of  11000  for  2  years.     Find 
rate  of  interest. 

17.  The  interest  on  11500  for  IJ  years  was  1120.     What 
was  the  rate  ? 

18.  The  interest  on  12000  for  3  years  was  $480.     What 
was  the  rate  ? 

19.  I  paid  13.60  for  the  use  of  1 60  for  6  months.     What 
was  the  rate  ? 

20.  I  borrowed  $100  for  1  year.     At  the  end  of  the  year 
it  amounted  to  $112.     What  interest  did  I  pay  ? 

21.  At  what  rate  will  $75  amount  to  $100  in  5  years  ? 

22.  $500  will  amount  to  $560  at  what  rate  in  2  years? 

23.  $124  in  1  year  and  6  months  amounted  to  $133.30. 
What  was  the  rate  ? 

24.  $1000  will  amount  to  $1024  in  3  years  at  what  per 
cent  ? 

25.  I  hired  a  certain  sum  of  money  at  6  ^  for  1  year.     The 
interest  amounted  to  $6.    What  was  the  sum  of  money  hired? 

26.  The  interest  on  a  certain  sum  of  money  for  2  years  at 
65^  was  $15.     What  was  the  sum  of  money  ? 

27.  I  paid  $21  for  the  iise  of  a  certain  sum  of  money  for 
1  yr.  9  mo.  at  6  ^.     What  was  the  sum  ? 

28.  What  sum  of  money  will  earn  $75  in  3  yr.  at  5^  ? 

29.  $42  is  the  interest  on  what  sum  of  money  for  2  years 
at  7fo? 

30.  $  60  is  the  interest  for  6  months  at  8  ^  on  what  sum  of 
money  ? 


192  ARITHMETIC   WITHOUT   A  PENCIL 

31.  How  many  dollars  will  amount  to  $  106  in  1  year  at  6  ^  ? 

32.  How  many  dollars  will  amount  to  f  275  in  2  years  at 

33.  What  sum  will  amount  to  $1024  in  3  years  at  8^6  ? 

34.  I  hired  a  certain  sum  of  money  for  2  yr.  at  Ifo.   When 
I  paid  it,  it  amounted  to  1128.     What  was  the  sum  hired  ? 

35.  What  sum  of  money  will  amount  to  1336  in  1  year 
4  months  at  9^? 

36.  I  hired  11000  and  kept  it  until  it  amounted  to  11050 
at  5fo.     How  long  did  I  keep  it  ? 

37.  A  man  hired  f  200  for  so  long  a  time  that  it  amounted 
to  $300  at  10  fo.     How  long  did  he  keep  it  ? 

38.  In  what  time  will  $150  earn  $2.50  at  5^  ? 

39.  How  long  will  it  take  $250  to  earn  $10  at  6^  ? 

40.  How  long  will  it  take  $425  to  amount  to  $467.50  at 
lOfo? 

220 

1.  Find  the  interest  on  $400  for  1  yr.  9  mo.  24  da.  at  6%, 

2.  Find  interest  on  $250  for  2  yr.  6  mo.  6  da.  at  10%. 

3.  Find  interest  on  $45  for  3  mo.  10  da.  at  5%. 

4.  Find  interest  on  $90  for  9  mo.  15  da.  at  6%. 

5.  Find  interest  on  $1000  for  2  yr.  20  da.  at  6%. 

6.  Find  interest  on  $500  for  63  da.  at  6%. 

7.  Find  interest  on  $50  for  7  mo.  at  8%. 

8.  Find  interest  on  $100  for  5  mo.  5  da.  at  6%. 

9.  Find  interest  on  $120  for  1  yr.  7  mo.  at  7%. 
10.  Find  amount  in  each  case  above. 


PERCENTAGE  193 

221 

1.  At  what  rate  will  160  earn  818  in  3  yr.  ? 

2.  At  what  rate  will  1800  amount  to  1950  in  1  yr.  6  mo.? 

3.  In  what  time  will  175  earn  $1  at  1%  per  month? 

4.  In  what  time  will  $100  amount  to  |150  at  6%  ? 

5.  What  sum  will  earn  §50  per  month  at  4%  per  year  ? 

6.  What  sum  will  amount  to  $1150  in  5  yr.  at  3%  ? 

7.  In  what  time  will  14000  earn  $100  at  6%  ? 

8.  What  sum  will  earn  $75  in  4  mo.  at  8%  ? 

9.  What  is  the  amount  of  $1  for  1  yr.  1  mo.  at  6%  ? 

222 

Find  the  number  of  days  on  the  calendar  from  : 

1.    Mar.  3  to  Sept.  7.  2.  Jan.  15  to  Aug.  13. 

3.    June  11  to  Dec.  7.  4.  Nov.  3  to  Feb.  10. 

5.    Aug.  9  to  Jan.  9.  6.  Dec.  20  to  May  10. 

7.    Oct.  8  to  Dec.  3.  8.  Feb.  3  to  Nov.  13. 

9.    Nov.  13  to  Feb.  3.  10.  Aug.  16  to  Mar.  24. 


$41.00.  Los  Angeles,  April  3,  1904. 

Six  months  after  date  I  promise  to  pay  to  Ernest  Davids, 
the  sum  of  Forty-one  Dollars,  with  interest  at  6%  per 
annum,  for  value  received.  Robert  McGovern. 

1.  Who  promises  to  pay  the  money  ? 

2.  What  is  this  written  promise  to  pay  called  ? 


19.1:  ARITHMETIC   WITHOUT   A   PENCIL 

3.  To  whom  does  he  promise  to  pay  ? 

4.  What  is  the  one  to  whom  the  note  is  payable  called  ? 

5.  Can  any  one  else  collect  the  money  ? 

6.  Where  is  it  payable  ? 

7.  What  amount  is  then  due  ? 

8.  What  is  the  face  of  the  note  ? 

1100.00.  •  Buffalo,  June  7,  1903. 

One  year  from  date  I  promise  to  pay  to  Ray  Craig,  or 
order,  One  hundred  Dollars,  with  interest  at  5  ^  per  annum, 
for  value  received. 

Harry  Ross. 

9.  Who  is  the  maker  or  drawer  ?  ' 

10.  Who  is  the  payee  ?     The  payer  ? 

11.  What  phrase  does  it  contain  that  the  preceding  one 
does  not  ? 

12.  What  difference  does  this  make  ? 

13.  What  is  the  date  ?     The  face  ? 

14.  What  is  the  date  of  maturity  ? 

15.  What  is  then  due  ? 

Read  the  above  note,  changing  the  place,  date,  face,  and 
interest,  and  making  John  Gordon  the  drawer  and  Ralph 
Lewis  payee.  Read  and  write  several  other  notes,  making 
yourself  drawer.  Tell  whether  or  not  the  notes  are 'negoti- 
able.    [Negotiable^  transferable.] 


PROPORTION 


195 


PROPORTION 
224 

15-^3=5.     45^9  =  5.     Therefore,  15  -^  3  =  45  ^  9. 
21-T-3  =  7.     56^    8  =  7.     Therefore, 


24  -  8  =  ?       27  - 
28  -  7  =  ?       44  - 

4.  108^9  =  ?     132- 

5.  21-  3 -=56^? 
7.  3^12  =  10-? 
9.     9-18=  ?  ^14 

11.      ?-    9  =  36^12 
13.   10-^30=    7^? 
15.      ?-^96=    2-V-16 


9 
11 
11 


Therefore, 
Therefore, 
Therefore, 

6.      3^15=  ? 


8.  121  -  ?  =  88  ^    8 
10.      7  -V-  ?  =  2  - 12 
12.      5  -^  ?  =  25  ^   5 
14.    32-   4  =  64-? 
16.    35^  ?  =42^    6 


45 


15  —  3  =  45  -^  9.      Another    way    of    expressing    1 
15  :  3  :  :  45  :  9.     This  is  read  :  15  is  to  3  as  45  is  to  9. 


this    is 


Read  these : 

24  :  36  :  J  10  :  15 

6  :  15  :  :  40  :  ? 

20  :  25  :  :  ?  :  20 

7:14::  5:? 

18  :  30  :  :  60  :  ? 

45  :  50  :  :  18  :  ? 

12  :  ?  :  :  15  :  45 

?  :  21  :  :  12  :  18 

14  :  24  :  :  21  :  ? 

21  :  42  :  :  ?  :  10 

9  :  ?  :  :  12  :  36 

Note  how  :  is  used  in  place  of  -^,  and  :  :  in  place  of  =. 
This  method  is  called  Proportion^  which  is  the  expression 
of  an  equality  of  ratios.  Ratio  means  relation.  The  relation 
of  15  to  3  is  that  of  5  to  1 ;  the  ratio  of  15  to  3  is  5  to  1. 
The  ratio  of  45  to  9  is  also  5  to  1.  Therefore  the  ratio  of 
15  to  3  is  the  same  as  the  ratio  of  45  to  9. 


196 


ARITHMETIC   WITHOUT   A   PENCIL 


The  ratio  of  3  to  15  is  J ;  of  9  to  45  is  ^.  So,  15  :  3  :  :  45  :  9 
and  3  :  15  :  :  9  :  45. 

15  :  3  or  3  :  15  is  the  first  ratio,  while  45  to  9  or  9  to  45  is 
the  second  ratio. 


Suppose  the  first  ratio  to  be  18  :  6,  and  the  numbers  in  the 
second  ratio  to  be  4  and  12.  What  is  the  order  of  the  num- 
bers in  the  second  ratio  ? 


1st  ratio. 

1.  5  :  25 

3.  42:48 

5.  7:    8 

7.  11:12 

9.  96  :  84 

11.  40:30 


Arrange  for  2d. 
(7  and  35) 
(63  and  72) 
Qm  and  64) 
(132  and  121) 
(  35  and    40) 
(  24  and    32) 


2.  25:  5 
4.  48:42 
6.  8:  7 
8.  65  :  5 
10.  21  :  27 
12.    100:120 


(7  and  35) 
(63  and  72) 
(56  and  64) 
(     6  and    78) 
(  35  and    45) 
:  :  (10  and  12) 


Solve  the  proportion ; 


(1)    (2)        (3)    (4) 

15  :  3  :  :  45  :  9.  15,  3,  45,  and  9  are  the  firsts  second^  thirds 
and  fourth  terms,  respectively.  The  first  and  fourth  terms 
are  called  the  extremes;  and  the  second  and  third  are  called 
the  means.  The  product  of  the  means  always  equals  the 
product  of  the  extremes; 


15:3 


:  45  :  9. 

1 

5  X  9  =  135 

15  :  3  :  : 

45 

:  ?  is  solved. 

15  :  3  :  : 

? 

:  9  is  solved, 

3  X  45  =  135,  hence: 


3  X  45_Q 
~1^-^ 
15  X  9 


45; 


15  :  ?  :  :  45  :  9  is  solved, 


PROPORTION  197 

15  X  9    "o 


45 


?  :  3  :  :  45  :  9  is  solved,  ^-^^  =  15. 
Solve  these  proportions  and  those  already  given 


1.  18:12::15:    ?  5.  20 :    ? 

2.  40  :  70  :  :   ?  :  28  6.  72  :  60 

3.  100  :    ?  :  :  50  :  55  7.  39  :  13 

4.  ?    :  18  :  :  18  :  12  8.  ?  :    4 


:  35  :  42  9,  ?  :  18  :  :  30  :  36 

:  42  :    ?  10.  54  :    ?  :  :  42  :  35 

:    ?  :    1  11.  14  :  42  :  :    ?  :  45 

:    9  :  12  12.  25  :  60  :  :  35  :  ? 


Mary  bought  3  pounds  of  candy  for  45  cents.  I  bought 
5  pounds  of  the  same  candy.     What  should  I  pay  ? 

The  same  relation  that  exists  between  the  weight  of  her 
candy  and  mine  should  exist  between  the  price  of  hers  and 
of  mine.  I  bought  more  candy  and  must  pay  more  than  she, 
therefore :   3  :  5  :  :  45  :  ? 

Before  stating  the  first  ratio,  you  must  always  ask  yourself 
the  question.  Is  the  answer  to  be  greater  or  smaller  than 
the  corresponding  given  number  ?  Then  arrange  both  ratios 
in  accordance  with  this  reasoning. 

1.  If  20  marbles  cost  30  cents,  what  will  30  of  the  same 
kind  cost  ? 

2.  If  5  pounds  of  candy  cost  75  cents,  what  will  12  pounds 
cost? 

3.  If  2  yards  of  ribbon  cost  25  cents,  what  will  6  yards 
cost  ? 

4.  If  8  yards  of  ribbon  cost  56  cents,  what  will  3  yards 
cost? 

5.  If  10  cows  cost  i  600,  what  will  7  cows  cost  ? 


198  ARITHMETIC   WITHOUT   A  PENCIL 

If  7  pounds  of  peaches  cost  105  cents,  how  many  pounds 
can  be  bought  for  85  cents  ? 

105  cents  is  to  85  cents  as  the  amount  105  cents  will  buy  is 
to  the  amount  85  cents  will  buy.     Therefore,  105  :  85  ; :  7  :  ? 

1.  If  25  yards  of  carpet  cost  f  30,  how  many  yards  can  be 
bought  for  i50  ? 

2.  If  the  railroad  fare  for  500  miles  is  $21,  $40  will  pay 
fare  for  how  many  miles  ? 

3.  If  it  cost  137  to  carry  a  certain  amount  of  freight 
60  miles,  how  many  miles  should  $60  carry  it  ? 

4.  If  it  cost  $28  to  transport  50  tons  of  freight  a  certain 
distance,  how  many  tons  should  $75  transport  the  same 
distance  ? 

5.  If  it  cost  $  40  to  build  15  rods  of  fence,  how  many  rods 
of  the  same  fence  cost  $25  ? 


1.  If  11  men  can  pick  30  boxes  of  fruit  in  an  hour,  how 
many  boxes  can  20  men  pick  in  the  same  time  ? 

2.  If  5  men  dig  40  ft.  of  ditch,  how  many  feet  should 
7  men  dig  in  the  same  time  ? 

3.  If  3  boys  dry  25  boxes  of  apricots  a  day,  how  many 
boxes  ought  10  boys  to  dry  in  the  same  time  ? 

4.  If  9  men  use  6  loaves  of  bread  a  day,  how  many  loaves 
would  5  men  use  ? 

5.  If  2  men  cut  15  cords  of  wood  in  a  week,  how  many 
cords  should  3  men  cut  ? 

6.  If  5  men  cut  16  cords  of  wood  in  a  week,  how  many 
men  would  be  required  to  cut  20  cords  ? 


PROPORTION  199 

7.  If  8  bales  of  hay  last  5  horses  a  month,  how  long 
should  10  bales  last  ? 

8.  If  12  men  dig  30  ft.  of  ditch  in  a  certain  time,  how 
many  men  would  be  required  to  dig  45  ft.  in  the  same  time  ? 

9.  If  8  persons  weigh  1000  pounds,  how  many  persons  of 
the  same  average  weight  would  weigh  750  pounds  ? 

10.    If  10  girls  make  25  yards  of  lace  in  a  given  time,  how 
many  girls  should  make  75  yards  in  the  same  time  ? 


1.  A  certain  flagpole  casts  a  shadow  40  ft.  long  at  the 
same  time  a  stake  3  ft.  high  casts  a  shadow  4  ft.  long.  How 
high  is  the  pole  ? 

2.  A  church  steeple  that  casts  a  shadow  60  ft.  long  at 
the  same  time  a  6  foot  pole  casts  a  shadow  5  ft.  long  is  how 
high  ? 

3.  How  tall  is  a  tree  casting  a  shadow  240  ft.  long,  when 
a  tree  12  ft.  tall  casts  a  shadow  15  ft.  long  ? 

4.  How  long  a  shadow  does  a  man  6  ft.  tall  cast,  when 
a  child  2 J  ft.  tall  casts  a  shadow  3  ft.  long  ? 

5.  At  a  certain  time  of  day  our  house  casts  a  shadow 
across  the  street,  which  is  60  ft.  wide.  At  the  same  time  my 
shadow  is  6  ft.  long,  while  I  am  only  5  ft.  tall.  How  high 
is  our  house  ? 


1.  If  it  takes  4  men  12  days  to  do  a  certain  piece  of  work, 
how  long  should  it  take  5  men  to  do  it  ? 

2.  If  20  men  require  11  days  to  build  a  certain  wall,  in 
what  time  should  15  men  build  it  ? 


200  ARITHMETIC   WITHOUT   A  PENCIL 

3.  If  3  men  do  certain  work  in  8  days,  how  many  men 
would  be  required  to  do  it  in  6  days  ? 

4.  Ten  men  did  certain  work  in  24  days.  How  many 
would  have  been  required  to  do  it  in  30  days  ? 

5.  If  18  men  can  do  a  certain  piece  of  work  in  5  days, 
how  many  additional  men  would  be  required  to  do  it  in 
3  days? 


i 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


LD  21-100m-9,'47(A5702sl6)476 


YB   17233 


■X" 


QA  /  03 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


